QA 
102 

W425 


JC-NRLF 


IN  MEMQRIAM. 

Professor  J.  Henry  Sengei 


ANSWERS 

TO 

'ENTWORTH  AND  HILL'S 

ARITHMETIC. 


T.     Kr»^    '  S< 


WENTWORTH'S 
SERIES    OF     MATHEMATICS. 


First  Steps  in  Number. 

Primary  Arithmetic. 

Grammar  School  Arithmetic. 

High  School  Arithmetic. 

Exercises  in  Arithmetic. 

Shortor  Course  in  Algebra. 

Elements  of  Algebra.  Complete  Algebra. 

College  Algebra.  Exercises  in  Algebra. 

Plane  Geometry. 

Plane  and  Solid  Geometry. 

Exercises  in  Geometry. 

PI.  and  Sol.  Geometry  and  PI.  Trigonometry. 

Plane  Trigonometry  and  Tables. 

Plane  and  Spherical  Trigonometry. 

Surveying. 

PI.  and  Sph.  Trigonometry,  Surveying,  and  Tables. 

Trigonometry,  Surveying,  and  Navigation. 

Trigonometry  Formulas. 

Logarithmic  and  Trigonometric  Tables  (Seven). 

Log.  and  Trig.  Tables  (Complete  Edition), 

Analytic  Geometry. 


Special  Terms  and  Circular  on  Application. 


ANSWEES. 


Art. 

45,  995; 

Art. 

49,  1110.87; 

Art. 

53,  1.2626906; 

398.8  ; 

1000; 

6.3834733. 

488.92  ; 
1689.91. 

1299.07; 

770.22  ; 

54,  7.603166; 
11.4093504* 

46,  1707.8; 

1342.17. 

6.7286717; 

3271.1  ; 
1945.66  ; 
3440.4  ; 

2018.44  ; 

50,  886.353: 
950.998  ; 
347.0759  ; 
724.8363  ; 

10.528675  ; 
3.2657244  ; 
21.712055; 
19.9922991 

8440.75. 

1694.6084. 

22.6276131 

47,  2372.64; 

52,  6.6452727; 

20.0826303. 

8794.95  ; 

7.7847491  ; 

55,  4.523467; 

3625.3  ; 

10.6313239  ; 

14.8237261 

2299.86  ; 

20.8266782  ; 

22.1157111 

2062; 

1.2272041  ; 

24.8583194 

1897.8236  ; 

1.2099648. 

10.2590772 

1900.01828. 

53,  1.30103; 

29.6490831. 

48,  6.64528; 

4.5861528  ; 

57,  1448.95; 

30,106.937; 

3.5282304  ; 

2393.60; 

2284.57828  ; 

19.0826303  ; 

1870.27  ; 

371.8273. 

16.5414467  ; 

2956.89  ; 

49,  848.87; 

6.0157063  : 

4267.58  ; 

1748.87; 

4.2070434  ; 

3950.41  ; 

3041.87; 

5.2839031  ; 

6570.39  ; 

959.87; 

3.2384788  ; 

3501.93  ; 

1000.87; 

8.485051  ; 

4064.96. 

M43594 


ARITHMETIC. 


Art 

69,  3  ;  3  ; 

75,  1802; 

78,  15.1683487;  95, 

73; 

7;  3; 

814 

0.3178372; 

115; 

3;  9; 

51; 

1.854102; 

128; 

14; 

118; 

0.317004; 

116; 

22; 

2482; 

0.5040172; 

264; 

22 

15,545; 

1.618034; 

284; 

70,  40  mi. 

N.;  1388. 

0.080936. 

297; 

$4. 

79,  2.3561945; 

320; 

73,  111; 

76,  $106.98; 

1.5707963; 

354; 

220; 

$87.69; 

0.7853981; 

369. 

301; 

$97.87; 

2.6179939;  96, 

58,  (59)  ; 

432; 

$141.73; 

2.0943951; 

89,  (90); 

553; 

$23.50; 

1.5707963; 

88,  (89)  ; 

602; 

$118.46; 

1.0471975; 

241,  (242); 

716; 

$307.92; 

0.5235987. 

180,  (181); 

876; 

$26.38. 

80,  0.618034; 

121,  (121). 

877; 

77,  7066; 

0.7961796;  97, 

1,2; 

9978; 

6975; 

1. 

2,3; 

4997. 

7287; 

81,  46. 

3,5; 

74,  333; 

2848; 

82,  19,418. 

4,  4; 

423; 

1747; 

83,  382. 

2,6; 

522; 

7276; 

84,  46. 

1,  7. 

5922; 

6987; 

85,  329.426.    98, 

6689  ; 

6399; 

6960; 

86,  4615.71. 

8334.68. 

6397; 

7391  ; 

87,  115,946.    99, 

7.9585202. 

7341; 

3251. 

88,  182,741.   100, 

0.80415828 

6550; 

78,  0.4233109; 

89,  3822.161.   101, 

609  gals. 

3086; 

0.2617994; 

90,  1,107,790.  102, 

12; 

3878; 

4.3761829; 

91,  $501.02. 

17; 

9334; 

2.1462729; 

92,  $72.17. 

13.37; 

2999. 

0.088907  ; 

93,  $235.56; 

15.8958; 

75,  195; 

2.976072; 

$180.37. 

100. 

119; 

1.6715398; 

94,  66  yrs.  ;    103, 

0.5; 

1822; 

3.1636232; 

45  yrs.,  11  mos., 

30  days. 

ANSWERS. 


Vrt.                     Art. 

103,  0.47;      116, 

439.726; 

122,  0.0065; 

0.468; 

74.2064; 

0.00012. 

0.4764; 

469.206. 

123,  $98.10; 

0.4764012.   117, 

3.1415928; 

$320.60; 

104,  3005; 

3.1415928; 

$608.40; 

2494; 

78.53981625. 

$784; 

1997;      118, 

34.5576; 

$1028.40. 

1484; 

37.6992; 

124,  $0.83625; 

428; 

40.8408; 

$19.5125; 

939; 

43.9824; 

$0.250875; 

1436; 

47.124; 

$4.73875; 

1949. 

24.596748; 

$0.529625; 

105,  31,385. 

29.068884; 

$3.62375; 

106,  §3.15. 

38.013156; 

$22.30; 

107,  $8138.25; 

38.013156; 

$23.13625; 

$7245.75. 

40.249224  ; 

$0.39025. 

108,  A.D.  899  ; 

42.485292. 

125,  262.5; 

A.D.  1087  ;   120, 

31.4159265; 

5467; 

B.C.  399; 

314.159265; 

2355; 

B.C.  347; 

3,141,592.65; 

0.48825; 

B.C.  382; 

$37.50; 

523,456; 

A.D.  70. 

$21.70; 

9.321102. 

109,  James,  1  more. 

$58.75; 

129,  1.570796; 

116,  555; 

$375; 

15.70796; 

369; 

$217; 

2.356194; 

462; 

$587.50; 

235.6194; 

342; 

$337.50; 

3.92699; 

1684; 

$512.50. 

0.392699; 

2560;      122, 

0.236; 

0.00392699; 

17,312; 

0.0236; 

578.838326; 

7122; 

0.00063.; 

5.78838326; 

14,256; 

0.078; 

672.300688  ; 

58.009; 

0.00431  ; 

67.2300688; 

28.8594; 

0.002331  ; 

0.0672300688 

ARITHMETIC. 


Art. 

129, 

Art. 

7.85398;      135, 

Art. 

4466.88.    144, 

7.02460  ; 

786.183398;    138, 

7.77546; 

20,000,001.06; 

0.786183398; 

0.777546; 

0.381966  ; 

749.269692; 

0.0777546; 

5000.000  ; 

0.00749269692. 

52.20292; 

3000.00. 

130, 

215.042; 

5.230204;   147, 

1.  $626; 

2.15042; 

5.167932; 

$624; 

1612.815; 

82.8089; 

$628; 

161.2815; 

8532.7315. 

$626. 

178.48486.     139, 

90.85041; 

2.  1346. 

131, 

0.98994952; 

230.52519; 

3.  16.011  bu. 

0.9998490152; 

4.6723068; 

4.  $52,976,000. 

0.99999043656; 

5.5190079; 

5.  767,340. 

1.0000003360552; 

6.1370379; 

6.  252,321.5. 

1.979894; 

3.136364; 

7.  $73.20. 

1.999975782; 

4.183564; 

8.  $43.42. 

2.0000040662; 

4.7108292;  148, 

1.78;  83; 

2.999824; 

366.509528. 

C9. 
•^  > 

4.99985252;    140, 

0.4853772; 

56. 

381.924; 

0.3000228; 

2.  3.013; 

0.38196664319; 

0.61685316; 

0.6710; 

0.61803335681. 

0.2371908; 

0.2084. 

133, 

63,231.52; 

1.679724; 

3.  2.0036; 

654.6528; 

1.038276; 

20.034; 

450.8847; 

2.1347172; 

20.033. 

309.89508. 

1.649826.   153, 

321; 

134, 

2,914,700;     141, 

34.109310; 

423; 

278,560; 

20.103747; 

282; 

99.9999; 

2.296; 

141  ; 

7854. 

4.74165; 

212; 

135, 

1584; 

11.647195; 

10.41  ; 

3696; 

0.110999; 

12.004  ; 

897.6; 

8.362134; 

1.21; 

3025.44; 

74538. 

0.144. 

ANSWERS. 


158,  1.  0.04286;        160, 

4. 

2.23613. 

Art. 

167,  6.  19||f  ; 

0.000027  ;      165, 

1. 

2. 

i; 

36,666.66667. 

2. 

684. 

0.5. 

2.  23.33333; 

3. 

1095. 

7.  2; 

1571.42857; 

4. 

330. 

2T7r; 

18.57143. 

5. 

236.4. 

i; 

3.  24.28571; 

6. 

6048. 

0.1126; 

0.00064; 

7. 

6700. 

0.01; 

0.01182. 

8. 

30.12. 

0.00011. 

4.  0.01545; 

9. 

0.9072. 

168,  1.  3.637813. 

0.05833  ; 

10. 

44.1. 

2.  0.00129. 

0.0025. 

11. 

215,240. 

3.  2.030. 

5.  91.66667; 

12. 

8516.6. 

4.  0.00007294. 

1.41667; 

13. 

217. 

5.  38.144. 

14.16667. 

14. 

3040. 

6.  0.00005677. 

6.  2266.66667; 

15. 

259. 

7.  6120.968. 

1133.33333; 

16. 

324. 

169,  1.  1; 

0.12364. 

17. 

22.5. 

10; 

7.  320; 

18. 

33.75. 

100; 

32;                  167, 

1. 

2; 

1000; 

3.2. 

4; 

10,000  ; 

8.  0.032; 

5; 

100,000  ; 

1.17778; 

0.5; 

1,000,000. 

0.00012. 

0.4015; 

2.  1; 

160,  1.  3.35977; 

0.90202. 

TV; 

1.75499; 

2. 

0.70710. 

T^O; 

94.66644  ; 

3. 

0.70710. 

TtfW  '» 

184.98040. 

4. 

3.14159; 

Tin5iF"o  i 

2.  1.76470; 

0.31831. 

i  _    . 

1.73410; 

5. 

0.54023  ; 

yirir^TTr  ; 

1.73210; 

0.60919; 

3.  1; 

1.73200. 

0.5; 

1; 

3.  0.0000254; 

0.33333. 

1; 

4.  1.41423; 

6. 

U$f  ; 

1  ;     i 

ARITHMETIC. 


Art. 

169,  4.  10,000: 

TT7  innr  '•> 
100; 

5.  TV;                  6.10; 

10;               yV; 

_    i       •              iQ. 

7.  1.030301; 
1.01; 
0.99009. 

100. 

10.                       1. 

EXERCISE  I. 

Page  63. 

17.  73.603891. 
18.  1426.8527. 

21.  19.0554; 
21.8365. 

23.  0.45763; 
99.99824. 

19.  61.942. 

22.  24.7183; 

24.  8.5125. 

20.  11.5111; 
7.51917. 

0.8531. 

25.  24.9914. 

Page  64. 

26.  20.6445; 

31.  9.0601;  0.002025;     37. 

0.02295; 

0.2412; 
0.0224. 

0.00006561; 
132.682214448064; 

2.25; 
0.1794. 

27.  10.30005; 
241.46387  ; 

0.438976.                    38. 
32.  0.000512. 

11,875; 
2894.53125; 

0.01004. 

33.  48.64;  0.01078; 

7.8125. 

28.  0.000006; 

8.8089.                        39. 

0.10720; 

453.646; 
0.43104. 
29.  0.343; 
0.03555. 
30.  1.13925. 

34.  149.7;  3.593;  7557. 
35.  10.932;  0.4575;  2760. 
36.  39,840;  1000;             40. 
10,000,000. 

20.41482; 
0.17857. 
0.06905; 
58,257.40365; 
338,983.05084. 

EXERCISE  II. 

1.  7.375.    3.  10.         6.  5.         9.  0.06.  12.  0.00112914. 

2.  6.  4.  5.555.    7.  20.     10.  0.202272.  13.  3. 

5.  1.  8.  9.       11.  0.0078. 


ANSWERS.  7 

Page  65. 

14.  13.  17.  0.0505.  20.  0.7557.  23.  2760. 

15.  19.04.      18.  0.00046.          21.  0.010932.          24.  116. 

16.  120.         19.  0.0003593.      22.  0.00004575.      25.  2.52. 


EXERCISE  III. 


1.  909.    4.  2.27083  mi.    6.  21.36288  ;   7.  96.248  in. 

2.42.    5.  3.4167  hrs.      6.36618.     8.336.13445. 

3.  935. 

Page  66. 

9.  350.25  Ibs. 

14.  $5934. 

17.  8857.98276  min. 

10.  260,078. 

15.  61. 

18.  14,925.37313. 

11.  601. 

16.  37.56097  min.  ; 

19.  $31.45. 

12.  $2184.91. 

49.67741  min. 

20.  $196.80. 

13.4032;  $3.24. 

21.  66,662.97. 

Page  67. 

22.  8590.10270. 

26.  3  dys.  ; 

28.  B.,  $46.36; 

23.  7.48051  ; 

6  dys.  ; 

0.,  $41.48. 

9.30917; 

6  dys. 

29.  $63.20. 

1.24445; 

27.  H.,  $0.54; 

30.  420  ;  50. 

3.38375. 

T.,  $0.90; 

31.  6000. 

24.  $8383.67. 

R,  $0.36. 

32.  24,780  Ibs.  ; 

25.  7068. 

25,620  Ibs. 

33.  708  Ibs.,  dry  ; 
732  Ibs.,  wet. 

34.  15.245  cu.  in. ; 
113.34863  Ibs. 

35.  1.81357. 

43.  39.3708. 


36.  7.49064.  39.  671,400,000  mi. : 

37. 7.50334.  l,080,684,000kro. 

38.  11,190,000  mi. ;  40.  449.43724. 
18,011,400km.       41. 431.03448. 

42.  0.2178. 
Page  69. 

44.  Divided  by  2. 


45.  It  is  increased  by  two  times  the  number  ;  not  any. 


ARITHMETIC. 


46.  It  is  multiplied  by  the  square  of  the  number ;  not  any. 

47.  It  is  multiplied  by  the  number ;    it  is  divided  by  the 

number. 

48.  1.21  sec. ;       343.4  sec. ; 
475.3  sec. ;     723.4  sec. ; 
183.7  sec. ;     1291.1  sec. : 

49.  Earth,  91,501,150; 
Mercury,  35,357,660 ; 


Venus,  66,116,960 ; 
Mars,  139,255,740 ; 


2470.6  sec. ;     14,270.5  sec. ; 

4528.7  sec. ;     77,469,335  sec. 
9093  sec. ; 

Asteroids,  248,560,000 ; 
Jupiter,  475,619,560 ; 
Saturn,  871,824,200; 
Uranus,  1,750,483,800; 


Neptune,  2,747,209,400. 


Page  73. 

1. 

5.427km; 

5. 

1.23km; 

10. 

391.94845"' 

5,427,000mm; 

123,000cm 

16m. 

542,700cm. 

6. 

12.30m; 

11. 

$11.59. 

2. 

6.853m;  685.3cnt; 

12,300mm. 

12. 

$45. 

0.006853ku\ 

7. 

172.718m. 

13. 

42.05m. 

3. 

4970cm; 

8. 

862.05m; 

14. 

$3.12. 

49;700ram; 

0.00083m. 

15. 

$0.014. 

0.0497km. 

9. 

365.6m; 

16. 

533.33m. 

4. 

l,240,000cm; 

1.852272"'; 

17. 

0.07. 

12,400,000mm. 

0.364896m. 

18. 

$147. 

Page  75. 


1.  185.4276ha ; 
1.854276qkm. 

2.  278.56ha. 


3-  1 

l,743,100qmm. 
4.  174.675qkm. 


5.  l,361,400qra 

6.  22,500qm. 


s;e  76. 


7.  137qcm. 


8.  357.1qmm. 


Page  77. 
1.  2,250,000ccm  2.  2.162875cbm. 


ANSWERS. 


1.  17001; 
157.8541. 

2.  9500ccm;  15C< 

3.  125,000ccra; 
0.125cbm. 


Page  78. 

4.  4.3188hl; 
0.43188cbm 

5.  3751;   375,000ccm. 

6.  734.15965 11; 
7.3415965P1; 
0.734159651cbm. 


7.  8.573412867cbm. 

8.  734,578.912ccm; 
734.5789121. 

9.  1.7315cbm; 
l,731,500ccm. 


1.  1730; 
341. 

2.  100. 


Page  79. 

3.  13.756g;  4.  346.P. 

0.013756kg.       5.  376.15kg. 


EXERCISE  IV. 


1.  109.59m. 

2.  $254.12. 

3.  57.625ra. 

4.  3.437m. 

5.  ll,282km. 

6.  3312km  ;  2860km  ; 
1600km;  3180km. 


15.  3.1416m. 

16.  260,752.8mm: 
ll,655.3mm; 
103,044.5""" 
326. 7mm; 
370. 7mm; 
525.0ffira; 
123. 5mm. 


Page  80. 

7.  5527.9km  ; 
6712.45km ; 
15,478.12km; 
21,953.66km; 
288,240.5km 

8.  $4.11;  $14.15. 

Page  81. 

17.  925,142,191,327m 

18.  40,005.1344kn\ 

19.  4.1155m; 
4.1155m; 
69.9635m. 

20.  17  nearly; 
18  nearly; 
4197  nearly. 


6.  677,800mg. 

7.  5800. 


9.  $113.63; 

$229.17. 

10.  $745.88. 

11.  $64.88. 

12.  $128.50. 

13.  $968.50. 

14.  $47.32. 


21.  0.31831. 

22.  100cm. 

23.  1.7507m. 

24.  0.94538m. 

25.  636.62m. 

26.  6.3662cm. 

27.  23.87325m 


10 


ARITHMETIC. 


1.  323qcm. 

2.  ll,200ha ; 
ll,144.659ha. 


EXERCISE  V. 
Page  82. 

3.  14.222ha  ; 
14.166ha. 

4.  0.169ha. 

Page  83. 


24.  99.84m 

25.  54m. 


31.  19. 

32.  $35. 


38.  $120, 

39.  $234.60. 


Page  85. 

26.  43.76m. 

27.  25m ;  $46.88. 


5.  15.639qm  ; 
33.914qm  ; 
40.152qin. 


6.  2.49126761ha  ; 

7.  $956.66  ; 

8.  572.5566qcm  ; 

2.4909024ha  ; 

$956.51  ; 

0.7854qm. 

2.4907176ha; 

$956.44; 

9.  48.275ha. 

7.47288761ha. 

$2869.60; 

10.  754.7694qcm. 

7.  $168.16; 

$59,167.61  ; 

11.  18cm  ; 

$168.14; 

$59,158.93; 

36m. 

$168.12; 

$59,154.54  ; 

12.  468qm  ; 

$504.42; 

$177,481.08. 

300qm. 

Page  84. 

13.  153.9384qcm 

17.  7696.92qcm. 

21.  1809.5616qm. 

14.  1017.8784qcm 

18.  48.275ha. 

22.  5026.56qm  ; 

15.  199.5119qm 

19.  153.9384qcm. 

706.86qm  ; 

16.  226.1952qcm. 

20.  1.505qm. 

»  4319.  7qm. 

28.  33.25m;  $70.66. 

29.  44.8m;  40cm  ;  $56. 


Page  86. 

33.  $73.88.  35.  $36.14. 

34.  $14.  36.  $19.95. 

Page  87. 

40.  1.6.  42.  96. 

41.  3.75.  43.  5.5. 


37.  $43.20. 


44.  72;  $18. 
45.42;  $5.88. 


ANSWERS. 
Page  88. 


46.  $1.49. 

47.  $19.21? 


48.  $7.56. 

49.  $0.97. 


50.  $3.85. 

51.  $129.02. 


11 


52.  $55.20. 

53.  $118.04. 


EXERCISE  VI. 

Page  89. 
1.  378ccm.     2.  73.416s.     3.  1375.6064hl.     4.  lll,424.1184k*. 

Page  90. 

5.  $4258.69.  8.  280.68hl ;  11.  0.7851. 

6.  1079.7571 ;  173.086hl ;  12.  4.1321; 
1079.757k-.            364.884hl.  0.3921. 

7.  445,341ccm  ;  9.  2.3701m  ;  13.  523.6ccm; 
445.3411 ;                9.2201hl.  0.0012ccm. 
4.45341hl.  10.  298.452ccm.  14.  3811.2ccra,  or  3.81121. 


15.  1749.5611,  or 
17.49561hl. 


Page  91. 

16.  145,782l. 

17.  223.42  min. 


18.  40.459  min. 

19.  0.903178cbm. 


EXERCISE  VII. 

1.  100k«;  73.8kR;  3.  264.404k*.  5.  259.380kg. 
1000k«;  0.001kg.         4.  274.980ks.  6.  955.24kg. 

2.  $5. 

Page  92. 

7.  7235k*,  or  7.235';  8.  2S.75k*.  9.  24. 

8464.95ks,  or  8.46495*.  10.  363.33m*. 

EXERCISE  VIII. 
Page  93. 

1.  0.833.  3.  79.249kJ?;  79.443k{?;  4.  64.1806K ; 

2.  678.11k«.  79.831^;  81.286k«;  66.6779^. 

82.159^. 


12 


ARITHMETIC. 


Page  94. 


5.  2.608.              8. 

8.953.                10.  1.0258 

;         13.  7.3. 

6.  5.1635k*.          9. 

7.309  ;                      1.0257. 

14.  2.317. 

7.  12.242k*  ; 

283.615kg  ;         11.  4.315. 

15.  2.789. 

12.215k*. 

295.765k*.           12.  1.723  ; 

16.  3.04. 

2.098. 

Page  95. 

17.  17.8ccm; 

18.  13.616  ;  13.588  ; 

19.  7.5. 

1.893. 

13.592;  13.599. 

EXERCISE  IX. 

1.  2.67kg;  18.67kg; 

2.  161.5kg.        4.  401; 

5.  90l; 

1.14kg;  0.38kg; 

3.  201;                  13.331 

;           $4.44. 

2.67kg;   18.67k*; 

1401  ;                5601. 

6.  $0.06  ; 

93.33k*. 

37401. 

$0.065. 

Page  96. 

7.  $11.50.      10.11. 

.2  min.         13.  40  min. 

16.  61  times. 

8.  7.                11.  6.588  min.      14.  2.5331  a  min 

.  17.  852.6k*. 

9.  $26.25.      12.  2.4984  dys.     15.  265.26. 

18.  $159.86. 

EXERCISE  X. 

Page  97. 

1.  46,609m. 

5.  $900,662.50. 

7.  41.145m. 

2.  5013. 

6.  $23,062,338; 

8.  12.16m 

3.  840. 

$7,391,775. 

9.  0.028cm. 

4.  $2,876,626.20. 

10.  2304.338kn  . 

Page  98. 

11.  6.24km.       13.  100ha ;  14.  54,200,000ha.   17.  1690. 

12.  19,277.2.         10,000a ;          15.  $20,991.60.     18.  $0.136. 

l,000,000qm.   16.  716.  19.  $300. 

20.  0.9972  x  14.0715ha  -  13.987ha. 


ANSWERS. 


13 


Page  99. 

21. 

121,000; 

24.  0.15869cbm. 

27.  3.646cbm. 

181.5", 

25.  10.547™. 

28.  196. 

22. 

0.283608a. 

26.  52501;  2.38m 

29.  1.6387cbm. 

23. 

14.6965s. 

Page  100. 

30.  4200. 

32.  1331ccm;  18,782. 

31.  1372.551'1; 

$4952.50; 

33.  29.532cbm. 

$148.58. 

34.  1.273kg. 

Page  101. 

35.  $0.602.  41.  $1.48. 

36.  3243.  42.  9m. 

37.  0.0434578kg.  43.  0.86207m. 

38.  1.911'.  44.  $8. 

39.  1.16ccm;  0.14ccm;  0.088ccm;  45.  6.06ccm. 
0.113ccm;  0.095ccm;  4.167ccm.  46.  154.943qcm. 

40.  $0.548.  47.  32.5624kg. 


48.  33.696k*. 

49.  18,966. 

50.  0.4615cbm;  $14.28. 


Page  102. 

51.  3624.145k*. 

52.  258.741;  12. 

53.  20.48cbm. 


54.  $993.30. 

55.  56,000. 

56.  101.1181. 


Page  103. 

57.  67.259kg;  16.72cm.  61.  10,472'. 

58.  7;   51. 

59.  0.42568cbm;  $0.518. 

60.  6.603m. 


62.  666.37qm. 

63.  0.032mm. 

64.  1.264;  $2,173,913.04. 


Page  10  i. 

65.  3846.15m  67.  1194;  $188.81. 

66.  1128.7878kg.  68.  0.890791;  434.2K 

69.  196.875kg. 


Page  105. 

70.  $71.96;  1504.11134kg.    72.  $25,608.96.    74.  $0.191. 

71.  $0.28.  73.  83.333m.         75.  $1378.13. 


14 


ARITHMETIC. 


EXERCISE  XL 


1.  2  X  2  X  37  ;  4. 
23  X  3  X  11 ; 

2  X  89  ;  3  X  61 ; 
1X173;  11X17; 
2X  173;   7x7x7. 

2.  2x3x5x7; 
1  X  353 ; 

25X  3x  5x  11;       5. 

3x7x11; 

23x3x7xllxl7; 

37x37; 

23  x  32  x  19. 

3.  13  X  19  ;  3  X  109  ; 
1X179;   1x83; 
53Xl7; 

13  X  181 ; 
1  X  2333. 


Page  110. 

3X5X11; 

23  X  3  X  7  ; 

22  X  3  X  179  : 
2x3x2777: 
3x107; 
3x11x47; 
2x19. 
2x41; 
3x43; 

23  X  32 ; 
2x3x  11; 
22  X  17 ; 
5x13; 

22  x  19 ; 
2x43; 
23Xll; 
2x71; 


6.  2  X  163  ;  24  X  23  ; 
24  X  29  ;  22  X  73  ; 
2  X  181 ;   5  X  73  ; 
2  X  5  X  73  ; 
2x3x7. 

7.  22x7x31;  33X37; 
2x3  X  137; 
2x673;  33X283; 
2  X  3  X  1039  ; 

2  X  32  X  13  ; 

8.  3X  193;  1X577; 
22x53;2x32x7; 
27  •  213  • 
2x32x5x7xl3. 

9.  7x1171; 
55;   74;   II3; 

32x7x  11x113; 

3  x  7  x  11  X  109, 


EXERCISE  XII. 


1.  22x 3x7x0.1; 
22xl9x0.1; 
22x33x0.01; 
24x32X  0.001; 

22x32x  0.001;  37x0.001; 
3x5x11x13x0.01. 

2.  2x73x0.1; 
32x29x0.01;  22x53x0.1; 
2x3x7x11x17x0.01; 
22x7xllxl7x0.0001; 
22x  13x0.00001. 


3.  3xl72x0.01;  - 
3x7x23x0.1; 
32X  11x101x0.01; 
23x32x7x0.01; 
33x5xllx0.001; 
23X33X  0.001. 

4.  11x317x0.01; 
22x34x0.1; 
3x5x11x31x0.001; 
23x89x0.1; 
41x73x0.001. 


ANSWERS. 


15 


EXERCISE 

XIII 

Page  112. 

1 

.3. 

7, 

,2. 

12.  14. 

17.  6. 

22. 

11. 

2 

.  13. 

8 

,3. 

13.  12. 

18.  14. 

23. 

21. 

3 

.4. 

9 

.  5. 

14.  21. 

19.  16. 

24. 

16. 

4 

.  9. 

10.  14. 

15.  4. 

20.  24. 

25. 

17. 

5 

.27. 

11, 

,  6. 

16.  9. 

21.  42. 

26. 

101. 

6.  2. 

EXERCISE 

XIV 

Page  115. 

1 

.37. 

5 

.  135. 

9.  809. 

13.  97. 

17. 

1. 

2 

.  105. 

6 

.352. 

10.  113. 

14.  93. 

18. 

56. 

3 

,8. 

7 

.345. 

11.  127. 

15.  108. 

19. 

387. 

4 

.  151. 

8 

.  107. 

12.  99. 

16.  59. 

20. 

2138. 

EXERCISE 

XV 

Page  116. 

1 

.57. 

3 

.247. 

5:  107. 

7.37. 

9. 

111. 

2.23. 

4 

.327. 

6.  449. 

8.  119. 

10. 

227. 

EXERCISE 

XVI. 

Page  118. 

1.42. 

11. 

297. 

21. 

630. 

31. 

288. 

41.  7560. 

2.24. 

12. 

1001. 

22. 

32,400. 

32. 

36,036. 

42.  2400. 

3.30. 

13. 

385. 

23. 

780. 

33. 

3570. 

43.  32 

,844. 

4.36. 

14. 

432. 

24. 

3600. 

34. 

5040. 

44.  40,480. 

5.  105. 

15. 

660. 

25. 

600. 

35. 

27,324. 

45.  23 

,400. 

6.  120. 

16. 

7920. 

26. 

210. 

36. 

2340. 

46.  576,576. 

7.  168. 

17. 

6720. 

27. 

2520. 

37. 

27,720. 

47.  181,875. 

8.60. 

18. 

1296. 

28. 

2310. 

38. 

228,150. 

48.  50 

,592. 

9.  96. 

19. 

1800. 

29. 

756. 

39. 

13,800. 

49.  29,029. 

10.  231. 

20. 

4704. 

30. 

6630. 

40. 

2736. 

50.  10 

,241. 

16  ARITHMETIC. 

EXERCISE  XVII. 

Page  119. 

1.  4664.  6.  27,869.  11.  7,577,304.  16.  37,219. 

2.  11,803.  7.  92,796.  12.  12,397.  17.  163,601,937. 

3.  141,036.  8.  14,385.  13.  164,808.  18.  250,641,677. 

4.  41,123.  9.  5967.  14.  3,295,313.  19.  34,573. 

5.  23,069.  10.  61,318.  15.  260,117.  20.  79,781. 

EXERCISE  XVIII. 

Page  122. 

1.  If.         4.  9T8T.  7.  14|f  .         10.  26^-2T-         13-  18^- 

2.  2|.         5.  13fV         8.  37.  11.  3f££.  14.  18|*. 

3.  61         6.  11.  9.  50ff.         12.  13.  15.  359." 

EXERCISE  XIX. 

Page  123. 


W- 


EXERCISE  XX. 

Page  124. 

l.f.          6.f.         11.  f  16.  ¥V  21-TVr-  26.  |f 

2.f         7.  |J.       I2- If         17.  TV  22.fif.  27.  ff 

3.  ii|.       8.  -\-         i3-  H-  18'  If •  23'  Iff-  28'    239439823!2-- 

4.  if       9.  T8g-.       14.  1.  19.  if.  24.  -j^-.  29.  -f^. 

5.  if.     10.  f^.       15.  iff.       20.  -^-2T-  25'  *i  30'  f • 


ANSWERS.  17 


EXERCISE  XXI. 

Page  125. 

Mi 

2.  Of. 
3.4. 
4.  15. 

5.  3.           8.  f  .         11.  l^f       14.  3TV 
6.  10.         9.  15.        12.  2f  .          15.  4^. 
7.  LI.       10.  1-^.     13.  3-1-.         16.  5£. 

17. 
18. 
19. 
20. 

4 

13. 

EXERCISE  XXII. 

Page  126. 

2     ^ 
3.  ^V 

4.6. 

5.  lOf       8.  f          11.  IsV        14.  f 
6.  451        9.  11.        12.  48T%.      15.  1-l^f  . 
7.  2.          10.  3f  .        13.  1|.          16.  llf 

17. 
18. 
19. 

8f 
I.3 

Page  127. 

20.  6^. 

21.  fw 

22.  f  . 

23.  _U.       25.  f.          27.  52^4T.     29.  32TV 
24.  8.         26.  2}f  .     28.  20^-.     30.  |f  . 

31. 
32. 
33. 

1 

EXERCISE  XXIII. 

2     ^ 
3   -$- 

4.2l 

5.  s            8.  i4       n.  27          14.   9 

o                              o  o                    6  o                          14 

6.  2.            9.  2.          12.  If          15.  li. 
7.  |i        10.  1££.     13.  7-1.          16.  3. 

17. 
18. 
19. 

2 
6^-. 

EXERCISE  XXIV. 

Page  129. 

1. 
2. 

14.0     20031  5     324                K     288     255     130     152 

3.  .10.0_10.A_200._!Afi.       g^  315  19690  90  665 
7. 


8"  tf,    f  ,    I-      9-  H-    A-    H-       10'  T4T-    T?8-    fV>    A- 


18  ARITHMETIC. 


EXERCISE  XXV. 

Page  131. 

1. 

2. 

9. 

2TV 

17. 

113^.    25.  Hf££. 

33. 

341i| 

2. 

li 

10. 

21T3T. 

18. 

llf        26.  114  £1-. 

34. 

Hi 

3. 

H- 

11. 

l*i 

19. 

2ff  .        27.  10|ff  . 

35. 

1^4- 

4. 

4. 

12. 

If- 

20. 

3_i_.        28.  ll^f. 

36. 

346^ 

5. 

4. 

13. 

i- 

21. 

85^-.   29.  14f|. 

37. 

29^\65 

6. 

4. 

14. 

li 

22. 

199^.   30.  18^. 

38. 

istfi 

7. 

6|. 

15. 

tf 

23. 

12TV     31.  8if  . 

39. 

294fg 

8. 

* 

16. 

19jf. 

24. 

8^-.     32.  lOfi 

40. 

465fi 

EXERCISE  XXVI. 

Page  133. 

i. 

61 

10. 

4*. 

18. 

41.          26.  4|^. 

34. 

H4« 

2. 

i 

11. 

4f 

19. 

2TV.        27.  lOfff. 

35. 

101T3, 

3. 

T9- 

12. 

H- 

20. 

4f  .          28.  ftft. 

36. 

2AV- 

4. 

6V 

13. 

« 

21. 

3M-        29-  2HM- 

37. 

4if- 

5. 

H- 

14. 

6-jV 

22. 

57^0..     so.  1193TV. 

38. 

TT9- 

6. 

H- 

15. 

2||. 

23. 

6^V       31.  H93T7-^-. 

39. 

y-1-6-. 

7. 

61. 

16. 

3H- 

24. 

6f.         32.  1193H- 

40. 

TrV- 

8. 

21. 

17. 

1  2  0 

25. 

lOii.     33.  248||. 

41. 

218 

T9TT- 

9. 

7f 

42. 

ToTF- 

EXERCISE  XXVII. 

Page  134. 

1. 

iff- 

6. 

25^7_ 

10. 

g463          14g  ~^   1 

18. 

llffl 

2. 

3ifJ 

.     7. 

344jf. 

11. 

441            15     151 
2000'                 Tow" 

19. 

3. 

If 

8. 

186T2T8T 

12. 

1_1_             16.   4    73_ 

20. 

25-5¥c 

4. 

27-f-g 

9. 

if 

13. 

8i-io-     17-  137ift- 

21. 

II^'T 

5. 

0. 

22. 

STOTT 

Page  136. 

9.  If.                12.  J?. 

15.  3f 

19.  f 

10.  If                13.  f 

16.  2|f. 

20.  20. 

11.  lO^V            14.  $. 

17.  185. 

21.  -g93 

18.    53 

22.  1.' 

ANSWERS.  19 

EXERCISE  XXVIII. 
l-*f       5.  If 

2.  T»¥.     e,  1-J-J-. 

3.  If.      7.  4TV 

4.  TV    8-  2AV 

EXERCISE  XXIX. 
Page  137. 

1.  f .  8.  3$.  14.  f .  20.  f  26.  f  32.  1. 

2.2$.         9.TV  15.2.  21.  TL  27.  If  33.^. 

3.  f  10.  2$.  16.  f  22.  ,,V  28.  T\.  34.  2f|. 

4.  If.  11.  3^.  17.  TV  23.  ffa.  29.  HG$Jf  35.  $$f$$. 

6.  1.          13.  m.      19.  1.      25.    76        31>  L  37.  7 

«j*  7U  o  yuo 

7.  ^  38.  |f|. 

EXERCISE  XXX. 
Page  138. 

i.  i         e.  s^Vu-     n-  i^Mto-  16-  so^vv  21-  if!- 

12.  104A7^.     17.  125MI.  22.  6^V. 


4.  lOiff.    9.  7^.          14.  lOOrdnp  19.  ^.        24. 

5.  50fi.     10.  20^-V¥o-  I5-  Mfa.       20.  1^. 


EXERCISE  XXXI. 

1.  0.875.  8.  9.0048046875.  15.  0.01875. 

2.  0.9375.  9.  11.00475.  16.  7.75. 

3.  0.28125.  10.  0.072.  17.  1.2. 

4.  0.36.  11.  0.00425.  18.  0.328125. 

5.  0.078125.  12.  0.9296875.  19.  14.8. 

6.  4.01375.  13.  0.0208.  20.  0.69384765625. 

7.  5.00015625.  14.  0.04296875. 


20 


ARITHMETIC. 


EXERCISE  XXXII. 
Page  139. 


1.  33.58125  ; 

2.  104.993809^1; 
3.65.324375; 

4.  46.2625;  46|i. 
5.9.16875;  9T2eV 

6.  3.71875  ;  3ff  . 

7.  6.2625  ;  6fi~ 


8.  2.775  ;  2 

9.  44.5125; 
10.82.8192; 

11.  3.1875;  3TV 
12.0.388125;  ^Vo 

13.  7.91875  ;  7  j^, 

14.  296.875  ;  296f 


EXERCISE 

XXXIII. 

Page 

141. 

1.  0.5. 

7.  0.00081. 

12.  0.380952. 

2.  0.45. 

8.  1113095238 

.     13.  0.39. 

3.  3.416. 

9.  910l85. 

14.  0.5285714. 

4.  0.183. 

10.  111142857. 

15.  2.22745098039215686. 

5.  3.35416. 

11.  0.267857142 

.     16.  5.230769. 

6.  2135. 

17.  Seven. 

Page 
18.  Five. 

142. 
19.  Two. 

EXERCISE 

XXXIV. 

Page 

143. 

1       2  7                              *7     Q  1    6  7                  1  *^       7  9                               "I  Q     ~|    5  9 

O     4  2  1                             Q13                          14.4117                          OOQ,  643 
9  9"0''                                «T'                                   ~3"7~0~'                                    2220' 

3.  53^^. 

9.  1T52-. 

15-  Hti             21-  5fH- 

4.  7fff$. 

10.  m- 

16-  5AW985-        22-  iyMfi 

5.  2||  jjjj. 

nQ     9 
*     TT~0"' 

17.  «ff  .                 23.  ^. 

6-  ITi-HlT- 

19     ^91 
1/5.  OTTTTT. 

ANSWERS.  21 

EXERCISE  XXXV. 
Page  144. 

1.  y^  G,  C.  M.  ;  14  L.  C.  M.     7.  5fi-  G.  C.  M.  ;  14,140  L.  C.  M. 
2.^  60  8.^W    u          2520 

3.&  10,530"         9.^  855 

"          20&     "  10.2Y\      V          460 

4620  11.  6y\      "          8085 


Page  145. 
13.    2737.  14.   77.  15. 

EXERCISE  XXXVI. 

;  rfffc;  «•  ^^o- 


22*;  3;  T\;  1^  ;  T\;  H;  -/¥;  12; 
8.60f;  2861;  |.  258  ;   ||i  ;  TV  ;  T4T  ;  &. 
9.3;  4;   If;   1J;    1^. 

Page  146. 

10.  *;  4;   1;   l&l.tt;   l^V  12-  »A-  13' 

11.  10^.  14. 
15.0.5;    0.75;    0.625;    0.1875;  0.5625;  0.9375;  0.428571 

0.25  ;  0.125  ;  0.875  ;    0.3125  ;  0.6875  ;  0.16  ;      0.5  ;  0.27 
0.3;    0.375;  0.0625;  0.4375;  0.8125;  0.83;      0.175. 

1^*  ITS  »  TOTIT  »  T¥0"  '  "2T  '  ¥9T93"  ' 


17.  5f  or  5.6.        19.  6.7.        21.  121|  or  A|A. 

18.  36|tf.          20.  401.        22.  47.917. 

23.  0.86;  0.27;  0.283;  0.384615; 
0.1142857;  0.736842105263157894;  0.1320754716981. 

24.  ^V     26-  0.09375;  0.00009375;  0.2297  ;  0142857. 

25.  -  27. 


22  ARITHMETIC. 

Page  147. 


28.  ft.  29.  3^fi  34.  7$H$  ;   6ft  ;   5^  ;   21T\V 

30.  G.  C.  M.  49  ;  35.  -1  39.  4£  f  . 

L.  C.  M.  3889277.  36.  10/yV.         40.  li^ff  . 

31-  tt,  T9T>  tf>  M.  «•  37.  f  .  41.  5TV-'  °    43.  Tyt. 

32.  22|f       33.  Tif  g.  38.  6.33403.       42.  f  .          44.  f 

45.  0.731343283582089552238805970149253  ; 

0.378;  0.84931506.  46.  30,  45,  75  (the  smallest). 

EXERCISE  XXXVII. 


1.  132  in.         2.  23,166  ft,        3.  5499  in.         4.  5,294,820  ft 

5.  1309  mi.  192  rds.  4  yds.  2  ft.  8  in.  6.  443,646  in. 

7.  1,754,676  in.  8.  45,112,320  in. 

9.  102  mi.  114  rds.  3  yds.  1  ft. 

10.  4  mi.    89  rds.  5  yds.  1  ft.  2  in. 

11.  137  mi.    36  rds.  3  yds.  1  ft. 

12.  3  mi.  217  rds.  4  yds.  1  ft.  3  in. 

13.  7920  in.  14.  3238  fath.  4  ft.  1  in. 
15.  5  ft.  4  in.         16.  27-^-  mi. 

EXERCISE  XXXVIII. 
Page  152. 

1.  120,058,848  sq.  in.  4.  1148  sq.  rds.  2  sq.  yds. 

2.  944  sq.  yds.  103  sq.  in.       5.  23,048,771  sq.  in. 

3.  73,830,400  sq.  rds.  6.  43,560  sq.  ft. 

7.  15  A.  148  sq.  rds.  2  sq.  yds.  2  sq.  ft.  40  sq.  in. 

8.  3  A.  28  sq.  rds.  9  sq.  yds. 

9.  14  sq.  rds.  10  sq.  yds.  7  sq.  ft.  110  sq.  in. 


ANSWERS.  23 

EXERCISE  XXXIX. 
Page  153. 

1.  202  cu.  ft.  4.  9  cu.  yds.  11  cu.  ft.  88  cu.  in. 

2.  1,175,183  cu.  in.  5.  19  cu.  yds.  20  cu.  ft,  706  cu.  in. 

3.  43  cu.  ft.  21  cu.  in.          6.  9|  ft. 

7.  $101.86. 

EXERCISE  XL. 
Page  154. 

1.  59  pts.  4.  233  qts.  1£  pts.  7.  0.8036  bu. 

2.  GO  bu.  5  qts.    5.  465  qts.  0  pts.  3T7T  gi.    8.  109,792  pts. 

3.  790  gi.  6.  1.244  cu.  ft.  9.  96  bbls.  23  gals. 

EXERCISE  XLI. 
Page  155. 

1.  4  Ibs.  9  oz.  9  dwts.  11  grs.  5.  123  Ibs.  7  oz.  5.2  drs. 

2.  15  1. 1.  9  1.  cwt.  44  Ibs.  6.  32,316  grs. 

3.  4  t.  5  cwt.  53  Ibs.  3  oz.  7.  905  Ibs.  4  oz.  11  dwt.  16  grs. 

4.  150  Ibs.  8  dwts.  13  grs.  8.  613  Ibs.  7££  drs. 

9.  45  t.  27  Ibs.  13  oz.  5  drs. 
10.  176  t.  5  cwt.- 48  Ibs.  5  oz.  13  drs. 
11.  7680  TV  12.  16  fl.oz.  5  fl.  drms.  20  n^. 

EXERCISE  XLII. 
Page  15G. 

1.  22,645  sec.  4.  8  dys.  14  lirs.  13  min.  12  sec. 

2.  544,324  min.  5.  151 ;  118;  286;  151  dys. 

3.  33  dys.  17  hrs.  27  min.     6.  151,200  min. 

7.  468,000  sec. 

8.  1600,  1656,  1880,  1924,  2000. 


24  ARITHMETIC. 

EXERCISE  XLIII. 

Tage  157. 
1.  9025".          2.  54?202".  3.  15°  46'.          4.  58°  57'  1". 

5.  90°,  120°,  (180°),  45°,  30°,  0°' 

6.  2815  geog.  mi. ;   3244.75f  stat.  mi. 

EXERCISE  XLIV. 

Page  158. 

1.  140,000  d.  7.  £303  10  s.  3  d.  2  far. 

2.  76,750  far.  8.  2813  g.  20  s.  10  d. 

3.  £119  Is.  9.  1193  crowns  6  d.  3  far. 

4.  2268  half  sov.  2  s.  7  d.  10.  $3.86. 

5.  6495  g.  10  s.  11.  $4.76. 

6.  £1,801,919  14s.  12.  $3.67. 

13.  £61  2s.  6  d. 

EXERCISE  XLV. 

Page  160. 

1.  15°  C. ;  12°  R.  8.  -  22°  F. ;  -  24°  R. 

2.  25°  C. ;  20°  R.  9.  llf°  F. ;  -  9|  R. 

3.  510°  C.  ;  408°  R.  10.  41°  F. ;  5°  C. 

4.  -  40°  C. ;  -  32°  R.  11.  59°  F. ;  15°  C. 

5.  -  20°  C. ;  -  16°  R.  12.  -  13°  F. ;  -  25°  C. 

6.  50°  F. ;  8°  R.  13.  394°  F. ;  3|°  R. 

7.  71|°  F. ;  17f °  R.  14.  - 17|°  C. ;  - 14|°  R. 

EXERCISE  XLVI. 

Page  162. 

1.  3  dys.  4  hrs.  34  min.  36  sec.        3.  £92  12  s.  1  d.  3  far. 

2.  245cu.yds.4cu.ft.1514cu.in.  4.  35 mi.  126 rds. 4yds.  1  in. 

5.  151  A.  55  sq.  rds.  29  sq.  yds.  7  sq.  ft.  34  sq.  in. 

6.  23  bu.  6  qts.  1  pt.  9.  84  Ibs.  2  oz.  14  dwt. 

7.  212  t.  6  cwt.  3  oz.  10  drs.        10.  41  gals.  1  pt, 

8.  243  gals.  1  qt.  1  gi.  11.  132°  30'  45". 


ANSWERS.  25 

EXERCISE  XLVII. 

Page  163. 

1.  34  Ibs.  9  oz.  18  dwt.  11  grs.   3.  7  cu.  yds.  3  cu.  ft,  1528  cu.  in. 

2.  1  pk.  4  qts.  1  pt.  4.  £27  18  s.  2f  d. 

5.  7  gals.  2  qts.  1  pt. 

6.  8  t.  5  cwt.  98  Ibs.  5  oz.  11  drs. 

7.  6  A.  9  sq.  rds.  174  sq.  ft.  26  sq.  in. 
8.  31°  37'  45".  9.  298  dys.  21  hrs. 

10.  202  rds.  4  yds.  3  in. 

EXERCISE  XLVIII. 
Page  164. 

1.  £249  4  d.  3.  33  Ibs.  8  oz.  4  dwt.  4  grs. 

2.  1391  gals.  1  qt.        4.  55  t.  6  cwt,  70  Ibs. 

5.  2740  bu.  2  pks. 

Page  165. 

6.  108  wks.  1  dy.  12  hrs.  24  min. 

7.  32  cu.  yds.  7  cu.  ft,  498  cu.  in. 

8.  3  sq.  mi.  553  A.  27  sq.  rds.  3  sq.  yds.  2  sq.  ft.  36  in. 

9.  5  mi.  258  rds.  3  yds. 

10.  10  yrs.  67  dys.  23  hrs.  45  min.  36  sec. 

11.  38,508  mi.  19  rds.  3  yds. 

12.  2147  Ibs.  9§43l97  grs. 

EXERCISE  XLIX.  , 
Page  166. 

1.  1  mi.  207  rds.  2  yds.  8  in.  2.  137. 

3.  8  wks.  1  dy.  7  hrs.  50  min.  2|f-£-  sec. 

4.  77.  5.  325. 
6.  7  sq.  mi.  264  A.  39  sq.  rds.            7.  7. 


26  ARITHMETIC. 

EXERCISE   L. 

Page  107. 

1.  256  rds.  3.  62  Ibs.  8  oz. 

2.  30  sq.  rds.  4.  13  ,9.  4  d. 

5.  261  rds.  4  yds.  1  ft.  6  in. 

6.  101  sq.  rds.  24  sq.  yds.  6  sq.  ft.  108  sq.  in. 

7.  26'  40".  10.  2  qts.  1  pt. 

8.  121  dys.  16  hrs.  11.  320  dys.  6  hrs. 

9.  5  qts.  12.  3  oz.  18  dwt. 

EXERCISE  LI. 
.  168. 


1.  23  A.  40  sq.  rds.  16  sq.  yds.  1  sq.  ft.  28f  sq.  in. 

2.  10  hrs.  30  min.  38f  sec. 

3.  15  dys.  10  hrs.  38  min.  51  sec. 

4.  34  rds.  2  yds.  4T\  in. 

5.  57  rds.  2  yds.  2  ft.  7.5936  in. 

6.  5  t.  6  cwt.  94  Ibs. 

7.  8  oz.  6  dwt.  2|  grs. 

8.  1  Ib.  6  oz.  13  dwt.  8  grs. 

9.  3  mi.  198  rds.  4  yds.  4|  in. 

10.  2  wks.  2  dys.  3  hrs.  35  min. 

11.  12  dys.  10  hrs.  31  min.  30  sec. 

12.  86  rds.  4  yds.  1£  in. 

13.  4  cwt.  72  Ibs.  4  oz.  9|  drs. 

EXERCISE  LII. 

Page  169. 

i-Hi     4-i     7-A-     10-i        13-8f^-   le.^ 

2.  Hi      5-  *i    8-  rb-    n-  2V       14-  *i-        ir 

3.  A  A.      6.  TV     9.  ff        12-  fV  15'Mi 


ANSWERS.  27 

EXERCISE  LIII. 
Page  170. 

1.  £0.815625.    3.  0.445  A.    5.  0.242.    7.  0.0311. 

2.  0.73  mi.      4.  0.3174.     6.  0.501.    8.  0.303. 


9.  0.148.  Pa8e  17L  10.  0.243. 

11.  5.128  (reckoning  365  days). 
12.  1.139.          13.  0.15433.  14.  0.03.          15.  0.4388. 


EXERCISE  LIV. 

Page  172. 

1.  18°  45'. 

4.  51°  23'  45". 

2.  32°  45'. 

5.  93°  7'  30". 

3.  77°  32'  30". 

6.  62°  3'. 

7.  272°  30'. 

8.  228°  48'  45" 

9.  37  min.  20  sec. 

10.  4  hrs.  42  min.  14.  6  hrs.  43  min.  3.6  sec. 

11.  3  hrs.  46  min.  24f  sec.  15.  8  min.  8T2?  sec. 

12.  7  hrs.  14  min.  lOf  sec.  16.  5  hrs.  40  sec. 

13.  8  hrs.  58  sec. 

EXERCISE  LV. 

Page  174. 

1.  (1)  12  h.  53  m.  34if  s.  P.M.   (7)  2  h.  22  m.  8  s.  P.M. 

(2)  12  h.  49  m.  43ff  s.  P.M.   (8)  4  h.  51  m.  36  s.  P.M. 

(3)  1  h.  55  m.  56  s.  P.M.     (9)  5  h.  53  m.  16^  s.  P.M. 

(4)  7  h.  45  m.  35  s.  P.M.  (10)  6  h.  9m.  40  s.  A.M. 

(5)  3  h.  50  m.  15  s.  A.M.  (11)  7  h.  3  m.  59-f  s.  A.M. 

(6)  5  h.  58  m.  59  s.  A.M.  (12)  7  h.  6  m.  20  s.  A.M. 

2.  (1)  11  h.  13  m.  54-ff  s.  P.M.   (7)  12  h.  42  m.  28  s.  A.M. 

(2)  11  h.  10  m.  8|f  s.  P.M.  (8)  3  h.  11  m.  56  s.  A.M. 

(3)  12  h.  16  m.  16  s.  A.M.  (9)  4  h.  13  m.  36T\  s.  A.M. 

(4)  6  h.  5  m.  55  s.  A.M.  (10)  (4  h.  30  m.) 

(5)  2  h.  10  m.  35  s.  P.M.  (11)  5  h.  24  m.  194  s.  P.M. 

(6)  4  h.  19  in.  19  H.  P.M.  (12)  5  h.  26  m.  40  s.  P.M. 


28  ARITHMETIC. 

3.  (1)  6  h.  57  m.  38|f  s.  A.M.  (7)  8  h.  26  m.  12  s.  A.M. 

(2)  6  h.  53  m.  52||  s.  A.M.  (S)  10  h.  55  m.  40  s.  A.M. 

(3)  (8  A.M.)  (9)  11  h.  57  m.  20-&  B.  A.M. 

(4)  1  h.  49  m.  39  s.  P.M.  (10)  12  h.  13  m.  44  s.  A.M. 

(5)  9  h.  54  m.  19  s.  P.M.  (11)  1  h.  8  m.  3f  s.  A.M. 

(6)  12  h.  3  m.  3  s.  A.M.  (12)  1  h.  10  m.  24  s.  A.M. 

EXERCISE  LVL 

Page  174. 

1.  (1)  71°  3'  30"  W.     (5)  112°  30'  W.  (8)  76°  50'  W. 

(2)  69°  50'  W.          (6)  73°  44'  45"  W.  (9)  90°  W. 

(3)  81°  7'  W.            (7)  83°  3'  W.  (10)  89°  33'  W. 

(4)  92°  12'  W.  (11)  77°  4'  W. 

EXERCISE  LVIL 

Page  175. 

1.  7.875  gals.        2.  £4  7  s.  6  d.        3.  7  gals.  2  qts.  1.5  pis. 

4.  £1  4  s.  Z$  d. ;  £1  10  s.  5£f  d. ; 

£3  13s.  7f$eZ.;  £495.  8|f  d. 

5.  17,983.504  sq.  yds.  11.  0.1051136  mi. 

6.  -l-  turpentine  ;  |  pt.  12.  66,036  in. 

7.  9104  yds.  2  ft.  5.952  in.  13.  4320  cu.  in. 

8.  4-iff  ft.  14.  16871  Ibs. 

9.  4.32  oz. ;  1890  troy  grs.  15.  0.84375  t. 
10.  1,  16.  472i  Ibs. 

17.  19  bu.  2  pks.  5.6  qts. 

Page  176. 
18.  312| bu.  19.  144  bottles.  20.  156  mi.  72  rds.;  8^^f  hrs. 

21.  24  hrs.,  nearly.     25.  $350.  29.  94.5  mi. 

22.  $209.83.  26.  0.0184  mi.          30.  13|  gross. 

23.  $46.94.  27.  0.9703125  A.     31.  $2554.50. 

24.  $120.59.  28.  3  qts. 

32.  The  former,  by  2  ft,  8.08  in.     35.  0.192. 

33.  0.07056  t.  36.  0.09375. 

34.  0.03  sq.  ch.  37.  11  hrs.  6  min.  40  sec. 


ANSWERS. 


29 


38.  A. 

41.  58  min.  14.91  sec. 

42.  3  hrs.  12  min.  24  sec 

43.  2  ft.  11.6125  in. 

44.  4  t.  1  cwt.  80T7r  Ibs. 
45.35. 

46.  The  former  ;  f$. 


Page  177. 

39.  3|fmi.  40.  $291.67. 

.  47.  4436  mi.  99  rds.  1  yd.  6  in. 

48.  $15,832.30. 

49.  8938iff. 

50.  88  yds.  =  -^  mi.  ; 

3  min.-  ^hr. 

51.  42  min.  4  sec. 


1.  43-£  mi. 

2.  10,800  mi. 


EXERCISE  LVIII. 

Page  178. 

3.  4655.637  mi. 

Page  179. 


6.  4ff  mi.  10.  4ff  sec. 

7.  6¥9¥  in.  11.  1  min.  43T%\  sec. 

8.  2£  min.  12.  -^  day  ;  T\  A. 

9.  2J-  min.  Page  m 

17.  $3922.20. 

18.  1T\\  pts. 

19.  1040|f§-  mi. 


4.  1173£  ft. 

5.  4A-  mi. 

13.  1  A.  120  sq.  rds. 

14.  156|  gals. 

15.  $5035.20. 

16.  12  hrs. 


20.  24  mi.  ;   1  hr.  44  min.  10  sec. 

21.  If  dys. 

22.  2if  dys. 


23.  1  hr.  58  min.  7^-  sec. 

24.  5T^T  hrs. 

25.  l-/¥  dys. 

26.  2|f  dys. 

31.  2 


Page  181. 


all. 


32.  992  bu. 

33.  18  girls  ; 
32  scholars. 

34.  26  boys  ; 

22  girls. 


4f|,A 

Page  182. 

35.  35.      36.  120.      37.  35. 
38.  18  dwt.  8  grs.  troy  ; 
oz.  av. 


. 

27.  T*7  hr. 

28.  56J  min.  ;  125  gals. 

29.  1  hr.  42  min.  51f  sec. 

30.  1  hr.  3  min.  34ff  sec. 
,  B  ; 


40.  l-j%. 

41.  $  13,200. 

42.  14,  ||,  ||. 
39.  A,  $21,000  ;  B,  $15,000  ;  C,  $9000. 


30  ARITHMETIC. 

Page  183. 

43.  $0.75.  46,  lOfjftjj-  Ibs.        49.  27  min.        52.  11  dys. 

44.  $2665.          47.  $1.44.  50.  $9.336.       53.  324. 

45.  $25.42.         48.  Tig\.  51.  611  A.        54.  90. 


Page  184. 
55.  300.         56.  7  mos.         57.  34fff          58.  16.         59.  500. 

Page  185. 

60.  20.  62.  4  clys.     64.  2  dys.    66.  6f  yds.     68.  1396T4T. 

61.  11,268.     63.  84.          65.  15.           67.  2|  ft.        69.  67|. 

70.  C  the  fastest;  A  41  sec.,  B  19TV  sec. 

Page  186. 
71.  $89.40.          72.  $  7573.36.  73.  $  1830.70. 

EXERCISE  LIX. 
Page  187. 

1  9  ft,  3.  13  A.  5.792  sq.ch.  5.  418  yds.  =  76  rds. 

2.  60  rds.  or  990  ft.  4.  3  ft.  6.  12  sq.  ft. 

Page  188. 

7.  5  sq.  ft.  21  sq.  in.  10.  27,648.  13.  344|  sq.  yds.  border  ; 

8.36.  11.  2  sq.ft.  81  sq.  in.    411-1  sq.  yds.  path  ; 

9.  15.  12.  $  15.20.  3500  sq.  yds.  grass. 

14.  28.2744  sq.  ft.  16.  16,060.6446  sq.  ft. 

15.  502,656  sq.  yds.         17.  132.7326  sq.  ft. 

Page  189. 

18.  258.5248    sq.  ft,  22.  60|  yds.  ;  63  yds.  ;  none  ;  |  yd. 

19.  28.2744  sq.  in.  23.  59|f  yds.  or  60  yds. 

20.  452.3904  sq.  in.  24.  17-J-  sq.  yds. 

21.  4  sq.  ft.  52.32  sq.  in.  25.  $43.70. 


ANSWERS.  31 

Page  190. 

26.  $45.00  or  $46.67.         29.  Lengthwise.  32.  $46.50 

27.  $  123.375.  30.  81|  sq.  yds.  33.  $4.26. 

28.  $194.79.  31.  199^  sq.  yds. 

Page  191. 
34.  $41.03.  35.  $12.75.          36.  $33.75.          37.  $62.50 

Page  192. 

38.  131;   40.  78.     43.  33.     46.  325.        49.  $9.94.  52.  $32.84. 
14|.    41.  162.  44.  140.  47.  $2.36.    50.  $1.80.  53.  $10.71. 

39.  233£.  42.  207.  45.  300.  48.  $14.85.  51.  $3.92. 

Page  193. 

54.  187.  56.  302.  58.  $0.80.  60.  $1.38. 

55.  83.  57.  123.  59.  $1.22.  61.  $0.79. 

Page  194. 
62.  810.          63.  3^  in.  64.  24|  thousand. 

EXERCISE  LX. 
Page  194. 

1.  16  cu.  ft.  72  cu.  in.       3.  15  cu.  yds.  16  cu.  ft.  1512  cu.  in. 

2.  38,016  cu.  ft.  4.  120f  cu.  yds.  5.  52|  cu.  ft. 

Page  195. 

6.  63  cu.  in.       8.  $855.          10.  2  ft.  8  in.          12.  259,200. 

7.  1512.  9.  If  yds.       11.  13i  ft.  13.  58£  ft. 

14.  72  sq.  ft.  48|  sq.  in.  16.  14,088.9375  or  14,088|f  t. 

15.  36  sq.  ft,  36  sq.  in.  17.  14,400. 

Page  196. 

18.  $194.79.          20.  45^-  Ibs.         22.  8  ft.  24.  7fi-  ft. 

19.  13i  ft.  21.  6|.  23.  $13.67.          25.  2|  ft. 


32  ARITHMETIC. 

Page  197. 

26.  76-f  bu.        29.  16|  ft.  31.  $1440.        33.  5ff  t. 

27.  156  bu.       30.  107.1  bu.       32.  26^.  34.  4278f  gals. 

28.  6i  ft. 

Page  198. 

35.  132^-  gals.  39.  4.90875  gals.  43.  0.267. 

36.  7ff  gals.  40.  2.18  qts.  44.  28.51. 

37.  840  cu.  ft.  41.  696.9116  cu.  in.  45.  0.859. 

38.  1484.406  gals  42.  15.708. 

Page  199. 

46.  1.728  cu.  in.  53.  3f|£  cu.  in.  58.  1162f 

47.  iff  oz.  54.  2.987  cu.  in.  59.  704,000. 

48.  16f  oz.  55.  93f .  60.  4-JL  Ibs ; 

49.  |4  pts.  56.  1  t.  31^  Ibs. ;  1.44  sp.  gravity. 

50.  253^2-  grs-          1  t-  8  cwt.  43f  Ibs.  61.  36^  t.  ; 

51.  G.912.  57.  3|fff in-  17,600. 

52.  6.983. 

EXERCISE  LXI. 

Page  202. 

1.  90.8161.  4.  111.2945km.  7.  192.496ks. 

2.  3.73248kg.  5.  4.890ha.  8.  8.98416hl. 

3.  38.6325cbm.  6.  36.2408t. 

9.  9  mi.  100  rds.  4  yds.,  nearly. 

10.  7  A.  66  sq.  rds.  2  sq.  yds.,  nearly. 

11.  15  cu.  yds.  23  cu.  ft.,  nearly. 

12.  107  qts.  liquid,  or  92  qts.  dry,  nearly. 

13.  535  gals.,  or  57  bu.,  nearly. 

14.  13  Ibs.  4  oz.  15  dwts. 

15.  6  cds.  80  cu.  ft.,  nearly. 

16.  74.75  sq.  yds. 

17.  1  t.  2  cwt.  7  Ibs.,  nearly. 


ANSWERS.  33 

18.  1  A.  136  sq.  rds.  16  sq.  yds.  23.  1312. 

19.  1.275cbm.  21.  2.795  mi.  24.  $1.47. 

20.  0.981  cu.  yds.  22.  444.5625  Ibs.  25.  $8.40. 

26.  206.029  Ibs.  or  93.437kg. 

27.  Water:  226.233  Ibs,  102.61*;  oil:  201.7575  Ibs,  91.5kg. 

Page  203. 

28.  349  Ibs,  158.277kg.  32.  45.721. 

29.  297.1738  Ibs,  134.9169kg.      33.  1  hr.  11  min,  nearly. 

30.  10.0277kg,  22.111  Ibs.  34.  17  t.  16cwt.  64  Ibs. 

31.  $20.87.  35.  13,616.64g. 

36.  15.786.          37.  $3.92.          38.  13,777.796*. 

EXERCISE  LXII. 
Page  205. 

1.6:9.         2.9:12.         3.8:9.         4.8:14.         5.  $7:  $9. 
6.  8  ft.  :  11  ft.          7.  5  :  3.  8.  f  yd.  :  f  yd. 

EXERCISE  LXIII. 

Page  208. 
1.  16  dys.        2.  11TV        3.  2320.        4.  $5.89.          5.  40£. 

Page  209. 

6.  2TV  sq.  ft.  9.  139  ft.  lly6^-  in.     12.  39£f  sec. 

7.  2f|  hrs.  10.  8.  13.  34^  sec. 

8.  17  ft.  1TV  in.       11.  If  hrs.  14.  9  min.  59|  sec. 

15.  5  wks.  3  dys.  21  hrs.  20  min.         18.  1  t.  4  cwt.  45£  Ibs. 
16.2673.  17.  $7435.78.  19. 32f 

Page  210. 

20.  0.8  Ibs.  23.  $4165.  26.  8|f  mo.    29.50. 

21.  2565  francs.     24.  13  yds.  27.  Iff  in.      30.  21,000. 

22.  2306.85  Ibs.     25.  89^1  cu.  in.    28.  T^  in.        31.  2ff . 


34 


ARITHMETIC. 


EXERCISE  LXIV. 

Page  212. 
4.  124  Ibs.  6.  14  dys. 


2.  $26.44.  • 

5.  1368  bu. 

7.  540. 

3.  $23,356.67. 

Page  213. 

8.  6027. 

13.  lOf 

17.  60m. 

9.  $1.575. 

14.  38  ft.  1.5  in. 

18.  1134.2776kg. 

10.  56,875  gals. 

15.  150  yds. 

19.  242.5  cu.  ft. 

11.  188|f  yds. 

16.  5f-f-  in. 

20.  3.8  cu.  ft. 

12.  3  hrs. 

EXERCISE  LXV. 


Page  215. 

1.  $3000,  $4000,  $5000. 

2.  150  t,  200  t,  225  t.,  240  t. 

3.  1155  Ibs,  1848  Ibs,  3850  Ibs.; 
3560  Ibs,  2225  Ibs,  1068  Ibs. 

4.  $2000;  $1600. 

5.  700  Ibs.;  21  Ibs. 

Page  216. 


6.  730ff  Ibs.  ;   206^  Ibs. 

7.  37,500kg  saltpetre, 
6250kg  charcoal, 
6250kg  sulphur. 

8.  10f . 

9.  746.46 ;  210.54. 


10.  66|  Ibs,  33^  Ibs.  12.  $45.60. 

11.  23.203g  oxygen,  76.797g  nitrogen. 


EXERCISE  LXVI. 

1.  $1333.33^,  A's;  $666.66f,  B's.     2.  $863.28^  $836.71f 

3.  $948,  A's;  $752,  B's;  $816,  C's. 

Page  217. 

4.  $710,  A's;  $1196.25,  B's. 

5.  $882,  A's;  $759.50,  B's;  $525,  C's. 

6.  $37.50;  $60;  $35. 

7.  $656,  A's;  $287,  B's. 


ANSWERS.  35 

8.  $1837.50,  A's;  $3311,  B's. 

9.  £36  15s.;  £14  14  s. ;  £14. 
10.  $1811.25,  A's;  $1794,  B's. 

EXERCISE  LXVII. 
Page  220. 

1. 13,257.     3.  1500  Ibs.  saltpetre,     4.  19.2  t.  7.  660. 

2.  25.55  t.        200  Ibs.  sulphur,        5.  350.46  cu.  ft.     8.  12% 
300  Ibs.  charcoal.       6.  6052. 

Page  221. 

9.  66.  13.  1T\%  loss.  17.  $2750.      21.  $216. 

10.  20ff  % .  14.  Tf T  of  1  %  •  18.  8% .  22.  13fi% . 

11.  3f|%.  15.6ft.  19.15%.         23.  9f%gain. 

12.  $12,500.  16.  5if%.  20.  7fi-%  water,  92£f  alcohol. 

Page  222. 

24.  $3.93f.  26.  $4.16f.  28.  14f  oz. 

25.  7^%  gain.      27.  6f%.  29.  $7.50. 
30.  5.4  t,  silver,  714.6  t.  lead.    31.  3038.936  t. 

Pages  223-224. 
32.30%.     33.28^%.     34.  35T5T%.     35.100$.     36.5^%. 

37.  3,510,000  ;  13  :  87.       39.  $6400  ;  $7200. 

38.  14f  %  ;   12|%.  40.  30  cents  ;  26f  cents. 

41.  $143.  44.  2||%.  47.  25%. 

42.  99^% .  45.  2H%  -  48.  If  Ibs. 

43.  2i|%.  46.  16|%.  49. 0.00125. 
50-  TTo  5  8 7£  gals,  oxygen,  100  gals,  nitrogen. 

51.  0.00129.       52.  96i||.         53.  ft  of  1  % .         54.  5f|  in. 

Page  225. 
55.  492-^f-  ft. 


36  ARITHMETIC. 

EXERCISE  LXVIII. 
Page  226. 

1.  §13.06.         4.  $40;  2560  bu.  9.  $210. 

2.  $64.88.         5.  $5047.64.     7.  $12,445.31.     10.  $6955.56. 

3.  $1-611.30.     6.  \\<J0.  8.  $869.05.          11.  $1.523. 

- 

Page  227. 

12.  im%-  15.  $13,770.  n.  $14,159.25. 

13.  6758.6.  16.  $141.  18.  58,536|f  Ibs. 

14.  37,951.2  Ibs. ;  $  128.05.  19.  $  195.07 ;  141.51562  t, 

EXERCISE  LXIX. 

Page  228. 
1.  $13.25.     2.  $56.25.     3.  $1001.     4.  812,266.67;  $214.67. 

Page  229. 

5.  $12,000.  8.  §6.25.  11.  $8425.  13.  $96. 

6.  $1040.  9.8363.75.       12.  $97,272.         14.  $1840. 

7.  $1836.       10.  (1)91500;  (2)  $750;  (3)  $1125;  (4)  $1125. 

EXERCISE  LXX. 

Page  230. 
1.  $96.79.       2.  $962,326.53.        3.  $3.866.     4.  $15,306.12. 

Page  231. 

5.  $6.  7.  $204.80.        9.  §4032.         11.81240.70. 

6.  $17,818.91.     8.  $1587.60.     10.  284%.         12.  §4869.12. 

13.  $1781.80. 

EXERCISE  LXXI. 

Page  233. 
1.  $95.94.  2.80.13.  3.  §8.46. 


ANSWERS. 


37 


4.  $183.33. 

5.  $327.25. 

6.  $1.60. 

7.  §12.91. 

8.  $13.19. 

9.  $7.56. 

10.  $3.88. 

11.  $51.16. 

12.  $62.04. 


Page  234. 

13.  $37.45. 

22.  $487.83. 

14.  $68.62. 

23.  $323.35. 

15.  $9.46. 

24.  $6980.12. 

16.  $28.18. 

25.  $166.98. 

17.  $54.27. 

26.  $548.22. 

18.  $16.69. 

27.  $1268.40. 

19.  $50.60. 

28.  $660.44. 

20.  $  10.29. 

29.  $12,474.55. 

21.  $483.28. 

30.  $11,481.45. 

Page  236. 

31.4^%. 

35.  4%,  nearly.    39.4%.                   43.4%. 

32.41%. 

36.  3f  %.                40.  6%,  almost.     44.  4  yrs. 

33.4|%. 

37.41%.                41.71%.                 45.  2  yrs. 

34.  6%. 

38.  4T%45-%  .            42.  7-ff  %  .     46.  6  yrs,  almo 

47.  3  mos.  9  dys.                         48.  25  yrs. 

49.  11  yrs.  8  inos. 

50.  3  yrs.  4  mos. 

51.  3  yrs.  9  mos. 

52.  3  mos.  2  dys. 

53.  3  yrs.  5  mos. 


Page  237. 

54.  $750. 

55.  $336. 

56.  $235.29. 

57.  $8520. 

58.  $411.43. 


59.  $1754.39. 

60.  $8423.14. 

61.  $9723.33. 

62.  $4090.91. 


63.  $750. 

64.  $816.896. 

65.  $5982.55. 


Page  238. 
66.  $286.15.          69.  $166. 


67.  $6050.99.        70.  $560. 

68.  $19,600.          71.  $8432. 

74.  7%,  nearly. 

75.  1  mo.  8  dys.         77.  $22,222.22. 

76.  $524.10.  78.  2  yrs.  10  mos.  3  dys. 
81.  3  yrs.  4  mos.  24  dys.  82.  $4.44. 


72.  $8520. 

73.  $27.53. 


79.  6ff%, 

80.  $47.57. 
83.  §10.20. 


38  ARITHMETIC. 

EXERCISE  LXXIL 
Page  241. 

1.  May  1/4,  112  dys.,  $16.33  ;  §733.67. 

2.  Mar.  4/7,  60  dys.,  $46.86;  $4278.64. 

3.  Apr.  6/9,  73  dys.,  $19.03;  $1321.67. 

4.  Apr.  19/22,  2  mos.  21  dys.,  $16.38;  $1439.92. 

5.  June  2/5,  3  mos.  19  dys.,  $75.78;  $4474.58. 


6.  Apr.  4/7,  3  mos.  6  dys.,  $110.46;  $5067.46. 

7.  Apr.  1/4,  48  dys,  $47.60;  $4712.40. 

8.  Apr.  14/n,  1  mo.  16  dys,  $25.78;  $1992.07. 

9.  June  25/28,  3  mos.  13  dys,  $8.61  ;  $660.48. 

10.  Mar.  20/23,  35  dys,  $48.34;  $8991.66. 

11.  Feb.  27/Mar.  2,  27  dys,  $0.96f ;  $214.031 

Page  243. 

12.  $865.65.  14.  $1207.19.  16.  $4558.23. 

13.  $1630.64.  15.  $4056.80.  17.  $1120.26. 

Page  244. 

18.  $478.09.  22.  $640. 

19.  $3059.28 ;  $275.34.  23.  $512.65  ;  $61.52. 

20.  $3909.48;  $351.85.  24.  $596.12;  $29.01. 

21.  $2348.02;  $68.48.  25.  $683.31 ;  $31.89. 

Page  245. 
26.  $390.31. 

Page  246. 
27.  $162.31.  28.  $283.71.  29.  $234.13. 


ANSWERS.  39 

Page  248. 

30.  $1547.73.  31.  $391.01.  32.  $525.58. 

33.  $293.39.  34.  $17.61. 

Page  250. 

35.  $433.02.      38.  $3.52.        41.  $303.77.        44.  $1441.47. 

36.  $703.31.      39.  $24.73.      42.  $125.  45.  $1078.43. 

37.  $195.69.       40.  $40.62.       43.  $1562.50. 

Page  251. 
46.  $220.84.  47.  $245.08. 

Page  252. 
48.  $3438.32.  49.  $3569.79;  $3633.04;  $3635.67. 

EXERCISE  LXXIII. 

Page  254. 

1.  $4395.          4.  $4723.50.          7.  $4650.         10.  24. 

2.  $2450.          5.  $1096.871         8.  $5200.         11.  971. 

3.  $3046.871    6.  $11,600.  9.  $5000. 

Page  255. 

12.  91|.  15.  $329.  18.  $754.  21.  $857.14. 

13.  $1188.         16.  $30,000.  19.  3f£f  %.       22.  $271.19. 

14.  $270.  17.  $9800.  20.9%. 

Page  256. 

23.  $366.15.      26.  51%.  29.  6-Jf%-  32.  $5635. 

24.  $390.           27.  5f%.                30.  4T%%.  33.  $4925. 
25.31^%.          28.  5T5T%.              31.  5-f-%.  34.  $5671. 

35.  831. 

Page  257. 

36.  116|.  39.  $7291.67.  42.  144. 

37.  1331;  150;  166|.          40.  117|.  43.  $56. 

38.  71%.  41.  31%. 


40 


ARITHMETIC. 


44.  $13  decrease. 

45.  $8  increase. 

46.  $100  increase. 

47.  $200  increase. 


Page  258. 

48.  $40  increase. 

49.  $5  increase. 

50.  $20  increase. 

51.  $50  increase. 


56.  $14.66^. 

57.  $5787.46. 

58.  $1024.06. 

65.  $  1500  loss. 

66.  31,  at  91 


Page  259. 

59.  90|. 

60.  95f  (nearly) 

61.  3%,  at  63; 

67.  $  180  loss. 


52.  $10  decrease. 

53.  $40  increase. 

54.  &tffe%. 

55.  84. 


62. 

63.  149f 
,  at  67J.   64.  58£. 

68.  $  10,000. 


EXERCISE  LXXIV. 
Page  261. 

1.  $1102.75.  2.31346.63. 

Page  262. 

3.  $1595.20.      6.  $946.08.        9.  $275.52.      12.  $519.31. 

4.  $491.38.        7.  $716.85.      10.  $1262.31.    13.  $10,117.62. 

5.  $1184.30.      8.  $800.52.      11.  $1138.81. 


EXERCISE  LXXV. 
Page  263. 

1.  $1548.14.          2.  $723.90.          3.  $2408.01. 


4.  £413  4s. 

5.  £28. 

6.  £821  185. 


Page  264. 

7.  $1563.31. 

8.  $1945.53. 

9.  7672.5  fr. 
13.  5026-^-  marks. 


10.  14,583.4  fr. 

11.  $686.65. 

12.  $2838.75. 


ANSWERS.  41 

EXERCISE  LXXVI. 
Page  265. 

1.  57fg.  3.  $1.02;  $0.34.  5.  $0.30|f 

2.  139ff  Ibs.         4.  $0.33f  6.  $0.47. 

Page  266. 

7.  1.256.  8.  1.171.  9.  57:  146.  10.  4  :  5. 

41.  1  :  1  :  5 ;   1:1;   1:5;   6  gals. ;  8  gals. ;   12|%. 

Page  267. 
12.  775ffg  lead  ;  2242V  tin. 

Page  268. 

13.  6  mos.  14  dys.  17.  31  dys.,  July  22. 

14.  57  dys.  18.  46  dys.,  Aug.  21. 

15.  41  dys.  19.  6  mos. 

16.  94  dys.,  Aug.  12.  20.  69  dys.,  Aug.  19. 


*  269. 

21.  Aug.  23,  1881 ;  $  749.93.        22.  July  23, 1881 ;  $  1934.83. 
23.  May  29,  Dr.  \  May  30,  Or. 

Page  271. 

24.  June  17,  1879.  26.  Aug.  27,  1880. 

25.  Mar.  13,  1883.  27.  Dec.  19,  1886. 

Page  272. 

28.  $38.06.         29.  $153.44.         30.  $96.85.         31.  $22.43. 
32.  $110.93. 

EXERCISE  LXXVII. 
Page  27(1 

1.  54.          3.  703.          5.  1829.  7.  6879.  9.  7.33. 

2.  89.          4.  142.          6.  354.2.         8.  147.  10.  29.72. 


42  ARITHMETIC. 

11.  1.4045.      13.  1.414213.     15.  0.547722.     17.  2.972092. 

12.  0.01446.    14.  2.236067.     16.  1.802775.     18.  0.948683. 

Page  277. 

19.  311.13.  20.  12  ft.  3  in.  21.  8  ft.  11  in. 

22.0.666666;  0.745355;    0.707106;    0.774596;    0.845154; 

0.866025;  0.816496;  0.912871. 
23.  45;  4.2;  1.42;  23.1;  14.3.          24.  5  ft.          25.  91  in. 

Page  278. 
26.  60  in.  27.  25  ft,  28.  9  ft. 


EXERCISE  LXXVIII. 
Page  283. 

1.  11.  4.  6.7.  7.  3.91.  10.  4.7117. 

2.  12.  5.  53.  8.  67.31.  11.  25,805. 

3.  2.3.  6.  127.  9.  0.1985.  12.  49.68. 

13.  2,1544;  1.5361;  2.0274. 

14.  1.7099;  0.8220;  1.9660;  0.9085. 

15.  35  sq.  ft.  75.84  sq.  in. 

EXERCISE  LXXIX. 
Page  285. 

1.  1:16;  1:64.  3.  1  :  2;  1:4.  5.  1:2.154. 

2.  8  :  9261  :  10,648,000.      4.  1  :  2.121.  6.  1  :  0.687. 

Page  286. 

7.  8.299ft.  12.  9:  16;  27:64. 

8.  5040  sq.  in.  13.  3.931  in. 

9.  10,648  cu.  in.  14.  12  ft.  7.19  in. 

10.  174.1  Ibs.;  6  ft.  4.6  in.        15.  150  rds. 

11.  1  :  0.693.  16.  1:0.63. 


ANSWERS. 


43 


EXERCISE  LXXX. 

Page  291. 

1. 

0.7781. 

9. 

1. 

3980. 

17.  8.3222  - 

-10. 

25. 

0 

.3222. 

2. 

1.1761. 

10. 

1. 

4771. 

18.  9.5441  -  10. 

26. 

1 

.2040 

3. 

1.3222. 

11. 

1. 

6232. 

19.  7.5441  - 

-10. 

27. 

8 

.7481 

-10. 

4. 

1.1461. 

12. 

2. 

6232. 

20.  7.6020  -  10. 

28. 

9 

.7993 

-10. 

5. 

1.5441. 

13. 

1.0791. 

21.  8.6990  -  10. 

29. 

0 

.2431. 

6. 

0.9542. 

14. 

1. 

7781. 

22.  1.0970. 

30. 

2.0212. 

7. 

0.9030. 

15. 

1. 

8751. 

23.  0.0970. 

31. 

8.0212 

-10. 

8. 

1.6902. 

16. 

0. 

8751. 

24.  1.5741. 

32. 

0.0212. 

EXERCISE  LXXXI. 

Page  292. 

l. 

0.9030. 

7 

.  0.1003 

13.  0. 

2258. 

19.  2.9579. 

2. 

1.3980. 

8 

.  0.3495 

14.  0. 

4660. 

20.  0. 

6361. 

3. 

3.3804. 

9 

.  0.0596 

15.  0. 

2045. 

21.  2.4465. 

4. 

3.8168. 

10 

.  0.1690 

16.  0.2415. 

22.  0.4730. 

5. 

2.5353. 

11 

.  0.1398 

17.  1.1650. 

23.  0.5243. 

6. 

3.4950. 

12 

.  0.0768 

18.  0. 

3904. 

24.  1. 

3280. 

25.  1. 

1569. 

EXERCISE  LXXXIL 

Page  294. 

1 

.  9.6020 

-10 

11. 

0.1761. 

21. 

0.4559.  . 

2 

.  9.4559 

-10 

12. 

1.1461. 

22. 

8.8539 

-10. 

3 

.  9.7781 

-10 

13. 

8.2219  -  10 

23. 

7. 

6320 

-10. 

4 

.  9.6320 

-10 

14. 

7.3980-10 

24. 

7.5441 

-10. 

5 

.  9.8539 

-10 

15. 

8.1461  -  10 

25. 

5. 

1707 

-10. 

6.  0.1461. 

16. 

1.8539. 

26. 

4.8293. 

7 

.  0.2219 

17. 

2.6320. 

27. 

5. 

9333. 

8 

.  0.3980 

18. 

6.6320  -  10 

28. 

4.1040. 

9 

.  0.3680 

19. 

1.2219. 

29. 

2 

8627 

-10. 

10 

.  0.5441, 

20. 

9.5441  -  10. 

30. 

7. 

1373. 

44 


ARITHMETIC. 


EXERCISE  LXXXIII. 

Page  299. 

1 

.  1.8451. 

13. 

2.8638. 

25 

.  966. 

37. 

0.6910. 

2 

.  2.0043. 

14. 

7.9428-10. 

26 

.  34,580. 

38. 

48.67. 

3 

.  2.5224. 

15. 

0.9074. 

27 

.  7.162. 

39. 

47.58. 

4 

.  3.5429. 

16. 

0.6991. 

28 

.  0.9982. 

40. 

2.349. 

5 

.  3.2709. 

17. 

9.5762-10. 

29 

.  0.0540. 

41. 

3.721. 

6 

.  3.8386. 

18. 

8.8494-10. 

30 

.  0.3593. 

42. 

61.21. 

7 

.  3.9957. 

19. 

8.5709-10. 

31 

.  0.0001051. 

43. 

0.6137. 

8 

.  3.6424. 

20. 

1.9951. 

32 

.  0.001019. 

44. 

464.9. 

9 

.  3.0457. 

21. 

7974. 

33 

.  416. 

45. 

212.4. 

10 

.  4.7660. 

22. 

16.13. 

34 

.  0.1549. 

46. 

0.8168. 

11 

.  4.8913. 

23. 

2.781. 

35 

.  2.559. 

12 

.  4.4790. 

24. 

10.21. 

36 

.  165. 

Page  300. 

47 

.  4.324. 

55. 

129.6. 

63 

.  0.4876. 

71. 

2.351. 

48 

.  0.2783. 

56. 

97.84. 

64 

.  0.006134. 

72. 

1.961. 

49 

.  0.001569. 

57. 

43.8. 

65 

.  17.76. 

73. 

1.97. 

50 

.  3889. 

58. 

5.153. 

66 

.  669.9. 

74. 

0.8834. 

51 

.  0.0006324. 

59. 

0.2061. 

67 

.  29.76. 

75. 

9.683. 

52 

.  0.06523. 

60. 

0.7285. 

68 

.  70.37. 

76. 

13.13. 

53 

.  13.28. 

61. 

0.0005336. 

69 

.  167.1. 

77. 

4.391. 

54 

.  2.684. 

62. 

0.629. 

70 

.  1.838. 

78. 

0.8578. 

Page  301. 

79.  2.534kg. 

80.  148.5 

sq. 

in.         81.  54.44 

in. 

82.  5.504 

in. 

EXERCISE  LXXXIV. 

Page  303. 

1. 

2.3028. 

4 

,  0.268; 

7. 

8.272. 

10. 

1.8117. 

2. 

22.11  ft. 

3.732. 

8. 

2.8541. 

11. 

1.186. 

3. 

6.828  +  ; 

5 

.  1.3713. 

9. 

9.1231; 

12. 

2.796. 

1.17+. 

6, 

,  2.8284. 

0.8769. 

ANSWERS.  45 

EXERCISE  LXXXV. 
Page  306. 


1 

1 

1 

1. 

Q     I 

1 

54-        ^ 

1 

O     J 
1 

+1 

1 

1  -1 

9  4- 

1 

3  -J- 

AJ   1 
1- 

1 

1 

1 

11 

i    1  • 

3.  i,  T4T>  «,  ft;  i  T4y,  H  -#A;  2,  f,  i  I,  if,  f 

4.  i  i,  I,  I,  A,  A,  if,  ft,  ft  ;    2,  1,  i,  «,  if  ,  i 

VM'Hf  Mi  TWIT- 
S' i  i.  i  AV  ;  1.  i  if  ,  tf,  iff  ;  i;  f  ,  I;  8,  8i,  8f  , 

6-  T76°A-  10.  1,  A»  tt  ft  - 

7-  1,  i  I,  A,  If,  H-  11.  1.  i  T85,  A- 

s.  i,  i  f  «,  tt,  *»-  12.  i,  f,  if, 

9-  i,  tt,  AV-  is-  1,  i,  i  i 


EXERCISE  LXXXVI. 
Tage  308. 

1.  15.  4.  25|.  7.  32,  431.  10.  If 

2.  72.  5.  9.  8.  5.  11.  1.1. 

3.  5^-.  6.  lOf  .  9.  6|.  12.  6. 

EXERCISE  LXXXVII. 
Page  309. 

1.  780.  5.  210.  9.  575. 

2.  74.  6.  765.  10.  209.3  ft,,  788.9  ft. 

3.  88.  7.  1200.  11.  32  mi. 

4.  103J.  8.  507.  12.  5|  mi. 


46  ARITHMETIC. 

EXERCISE  LXXXVIII. 

Page  311. 

1.  4374.  4.  |ff.  7.  248.832. 

2.1  5.  2441if.  8.  $1464.10. 

3.  22-lf  .  6.  7,  14,  28.  9.  $  1338.12  (by  logs)  ; 

$1338.23  (exact). 

EXERCISE  LXXXIX. 
Page  313. 

1.  728.  5.  l|f|f  8.  11,718. 

2.  511.  6.  Ifll  9.  4fff 

3.  363.  7.  l^ffi  10.  $  7254.40  (iy  logs)  ; 

4.  98ff.  $7253.13 


EXERCISE  XC. 

Page  314. 

1.1.  3.f  5.1|.  7.1. 

2.2.  4.1  6.  |f  8.  f|.  l 

EXERCISE   XCI. 

The  logarithm  of  a  power,  obtained  by  multiplication,  is  neces- 
sarily liable  to  an  error  in  the  last  place,  which  may  equal  half  the 
exponent.  A  result  thus  obtained  from  4-place  logarithms  may  there- 
fore be  uncertain  in  the  fourth  significant  digit. 

Page  316. 

1.  $82.08.  5.  4.38  yrs.  9.4.1% 

2.  $173.  6.  14.29  yrs.  10.  $852.80. 

3.  11.8  yrs.  7,  5.95$.  11.  $1352;  $3656. 

4.  18.9  yrs.  8,  7.6%  12.  $1197.50. 


ANSWERS.  47 

Page  317. 

13.  $1227.80.  15.  $2428.  17.  $2376. 

14.  $4818.  16.  $2647.  18.  $2418. 


CHAPTER  XXV. 

MISCELLANEOUS   PROBLEMS. 

Page  318. 

1.  123,  132,  213,  231,  312,  321 ;  1332. 

2.  235,  253,  325,  352,  523,  532;  1,892,000,000,000,000;  (by 

logs). 
3.873,  837,  783,  738,  387,  378;    61,770,000,000,000,000; 

(by  logs). 

4.2.093;  2.987;  3.741;  8.984;  (by  logs). 
5.0.4309;  13.98;  2.801;  1102.5;  (by  logs). 

6.  201.1 ;  4.39  ;  (by  logs).         8.  5268.585  ft,          10.  29.67. 

7.  1533.623  ft.  9.  808.97  ft.  11.  55.31. 

Page  319. 

12.  P.  200;  C.  101;  B.  189. 

13.432  =  54x8;  4  +  3  +  2  —  9;  3  +  4  +  2-6  +  3. 

14.  196.     15.  |£ff  19.  7974  dys. 

16-  ii  rl  If,  m-  20.  12  ft. 

17.25,  9,  49;  21.  3  mi.  160yds. 

225,  1225,  441,  11025.  22.  38  barges. 

18.  92  ft. 

Page  320. 

23.  458.491;  13.  bu.  29.  146  balls  (by  logs). 

24.  2803.194kg.  30.  0.00336  in. 

25.  1.3939  t.  31.  7  dwt.  21  gr. 

26.  1052.09  sq.  in.  32.  $2250. 

27.  7.407  A.  (by  logs).  33.  15  cts.  per  Ib. 

28.  523.6;  4188.8;  1:8.  34.  $13.85,  $8.85,  $4.42^. 


48  ARITHMETIC. 

Page  321. 

35.  12,480.          39.  15.2498;  15.25;  (by  logs).  43.  28T4T. 

36.  $15  a  year.  40.  A  gains  $5.05.  44.  9  men. 

37.  17^  min.       41.  905  t.  1392  Ibs.  45.  SOsq.in. 

38.  12£  min.       42.  46.37  sq.  in. 

Page  322. 

46.  1367  sq.  ft.  (by  logs).  49.  0.8908  A.  (by  logs}. 

47.  0.1467ha  (by  logs).  50.  224.3  A.  (by  logs). 

48.  0.2736ha  (by  logs).  51.  25.12  sq.  rds.  (by  logs). 

52.  3.946  A.  (by  logs). 

Page  323. 

53.  0.194167ha.    55.  866.0254  ft,    57.  61,785  sq.  ft.  (by  logs). 

54.  0.6436  A.      56.  13.2mm;  17.62mm;  23.36" 


Cmm 


Page  324. 

58.  Diagonal,  351.489  ft.;  area,  61,785  sq.  ft.  (by  logs). 

59.  314.16  sq.  in.;  78.54  sq.  ft,;  71.62  sq.  in. 

60.  0.2428ha.  63.  1922.9  sq.  in. 

61.  2205.5  sq.  ft.  (by  logs).         64.  50.2656  sq.  in. 

62.  9804  sq.  ft.  (by  logs).  65.  523.6  cu.  in. 

66.  Diam.,  5.57  ft.;  area,  24.37  sq.  ft.  (by  logs);  sphere, 

90.52  cu.  ft.  (by  logs). 

67.  Iron,  38.86kg,  85.66  Ibs.;    tin,  8.383kg,  18.48  Ibs.;    lead, 

30.76kg,  67.83  Ibs.;  silver,  0.01233kg,  0.02717  lb.;  (by 
logs). 

68.  898  balls  of  a  diameter  2.436  in.  (by  logs). 

Page  325. 

69.  3737.5  Ibs.  (by  logs). 

70.  Weights:      482.24mg,      482.24g,      482.24kg;      surfaces: 

3.1416qcm,  314.16qcm,  31,416qcm.  The  first,  if  we  take 
no  account  of  the  retardation  of  the  air  by  friction  on 
the  plane. 


ANSWERS.  49 

71.  End,  78.54  sq.  in. ;  convex  surface,  376.99  sq.  in. ;  total 
surface,  534.07  sq.  in. ;  contents,  4.08  gals. ;  (by  logs), 

72.  8935  gals,  (by  logs), 

73.  5.424  in.  (by  logs). 

74.  552.92  cu.  in. 

75.  6.65  in. ;  4.19  in. ;  10.84cm  ;  (by  togs). 

Page  326. 

76.  31.952  cu.  in.      78.  59,259Y7T  cu.  yds.      80.  15.09  cu.  in. 

77.  50.93  bu.  79.  66,966f  cu.  yds.        81.  2,614,689cbm. 

Page  327. 

82.  0.140671.  85.  112.071.  88.  178.3  gals. 

83.  98.47cm  radius.       86.  3.302  qts.  89.  22.286  gals. 

84.  1.8331.  87.  0.796  pt. ;  2.489  pts.;  3.825  pts. 

90.  0.249  pfc.;  0.963  pt;  2.002  pts. ;  (by  logs). 

91.  4.596  pks.;  0.531  pk.;  4  pks.;  (by  logs). 

Page  328. 

92.  10  ft.;  20  ft.  94.  112.8m;  564m;  (by logs.) 

93.  235.5  ;   706.5  ft. ;  (by  logs).     95.  25. 

96.  261.8  cu.  in.,  a  little  over  9  pts. 

97.  $78.54. 

98.  633  million  million  million  bu. ;  458  hundred  thousand 

million  yds. ;  (by  logs). 

99.  8  billion  cu.  mi.  (by  logs). 

100.  "  2  feet  square  "  means  a  square  2  ft.  on  a  side ;  "  2  square 
feet,"  any  surface  equivalent  in  area  to  two  squares 
each  1  ft.  on  a  side.  A  "foot  square"  is  a  square; 
while  a  square  foot  is  an  equivalent  area  in  any 
shape.  "Half  a  foot  square"  is  ambiguous.  Half 
"a  foot  square''  is  half  a  square  foot,  while  "half 
a  foot"  square  is  6  in.  square  ;  that  is,  is  one-fourth 
a  square  foot. 


50  ARITHMETIC. 

Page  329. 

101.  25-J-  cu.  ft.  103.  210.54hl. 

102.  4.42  qts.  104.  69.115  sq.  in. ;  247.401  sq.  in. 
105.  30  ft. ;  100  ft. ;  60  ft. ;  4712.4  sq.  ft. 

It  is  plain  that  the  kid  can  go  10  ft.  beyond  each  stake  on  a  line 
joining  them,  so  that  her  range  is  100  ft.  long.  When  she  is  at  the 
middle  of  the  cord,  and  draws  it  taut,  imagine  a  stone  midway  be- 
tween the  stakes.  The  stone,  the  kid,  and  either  stake  then  make  a 
triangle,  right-angled  at  the  stone ;  and  502  -  402  «  900  =  302,  so  that 
the  kid  is  30  ft.  from  the  stone  ;  the  width  of  her  range  is  therefore 
2  x  30  =  60  ft.,  and  its  area  4712.4  sq.  ft. 

106. 


i  330. 

107.  11  in. ;  13.603  (by  logs)  ;  117.5  sq.  in.  (by  logs). 

108.  9.784  in. ;  2.446  in. 

The  law  of  \  452  may  be  put :  The  length  of  pendulums  is  in- 
versely as  the  square  of  the  number  of  their  vibrations  in  a  given 
time.  Therefore,  a  half-seconds  pendulum  will  be  \  x  J  =  }  the 
length  of  a  seconds  pendulum  ;  and  a  quarter-seconds  pendulum, 
J  X  J  =  yV  the  length.  It  will  be  understood  that  these  lengths, 
39.138,  9.784,  2.446  inches,  refer  to  the  theoretical  case  in  which  the 
rod  is  without  weight  and  all  the  weight  on  the  end ;  or  they  are  the 
distance  apart  of  two  points  in  a  bar  of  uniform  thickness  and 
weight  from  end  to  end,  at  either  of  which  the  rod  would  vibrate  at 
the  required  rate. 

109.  55.92cm;  397.64cm.  110.  8.17  times. 

111.  1,000,000^. 

Suppose  the  plunger  and  piston  square:  the  one  would  p^ess  on  a 
surface  of  l<icm,  the  other  on  a  surface  of  10,000<icm.  By  driving  the 
plunger  in  10cm,  you  force  10ccm  of  water  under  the  piston.  But,  as 
this  is  spread  under  10,000<icm,  you  raise  the  piston  thereby  only 
0.001cm;  that  is,  only  0.0001  part  of  the  way  you  move  the  plunger. 
Hence,  by  the  principle  of  virtual  velocity  (what  is  lost  in  time  is 
gained  in  power),  you  lift  the  piston  with  10,000  times  your  force 
of  100ks  applied.  The  lifting  power,  in  other  words,  is  1,000,000^, 
or  1000*,  minus  the  trifling  loss  by  friction. 


ANSWERS.  51 

112.  9,216,000  Ibs.  113.  144,000  Ibs. 

Page  331. 

114.  114  t.  ;  6  t.  ;  600  t,  115.  56^  t.  of  2000  Ibs. 

116.  7.355m;  31.869m  per  sec. 

As  the  velocity  is  in  proportion  to  the  time,  the  velocity  in  J  of  a 
second  will  be  f  X  (9.806™),  that  is,  |  X  (32.172  ft.)  =  24.139  ft.  ;  in  3J 
seconds  it  will  have  a  velocity  of  3J  X  32.172  =  104.56  ft.  per  second  ; 
that  is,  that  will  be  its  rate  at  that  instant,  but  the  velocity  steadily 
increases.  In  the  first  tenth  of  a  second  a  stone  falls  0.1609  of  a  foot, 
but  has  already  acquired  a  velocity  that  would  carry  it  3.217  of  a 
foot  in  a  second.  In  the  next  tenth  of  a  second  it  goes,  therefore,  by 
that  velocity  0.3217  ft.,  and,  by  still  falling,  0.1609  more,  so  that  it  has 
gone  0.4826  of  a  foot  ;  and  its  velocity  is  its  old  one  and  3.217  added, 
that  is,  6.217  feet.  In  other  words,  the  falling  body  cannot  fall  so  fast 
as  to  lessen  its  weight  ;  its  weight  constantly  accelerates  its  motion. 

117.  0.3876  sec.  (by  logs). 

118.  198ra  per  sec.;  20.19  sec.  (by  logs). 

119.  651.8  ft.  per  sec.  ;  20.26  sec.  (by  logs). 


120.  3.81  sec.  §   332' 

The  acceleration  32.172  is  for  a  vacuum,  32  ft.  is  near  enough  for 
practical  questions  ;  and  16  ft.  for  the  fall.  V210  -^  Vl6  =  3.623  sec. 
will  therefore  give  the  time  of  falling.  To  this  add  -fffo  for  the 
sound  to  come  up,  and  we  have  the  answer  3.811  sec. 

121.  11.428  sec.  122.  747  ft.  123.  133  ft. 

124.  0.04515  sec.;  0.07198  sec.;  0.1428  sec.;  0.17635  sec. 

125.  24  ft.  per  sec. 

The  velocity  will  be  to  32  ft.  as  V9  is  to  VB;  that  is,  it  will  be 
24  ft.  a  sec.  This  law  is  obtained  from  experiment. 

126.  40  ft.  and  80  ft.  per  sec.  127.  15  gals,  an  hour. 

128.  GJ  gals. 

Page  333. 

129.  3  gals,  to  area;  3  pts.  to  friction. 

130.  3f  as  much  ;  15-J  as  much. 


52  ARITHMETIC. 

131.  6135  times  the  weight  of  the  material. 

Three  inches  in  diameter  is  1.5  in.  or  J  ft.  radius.  Therefore,  by 
the  formula,  the  outer  layer  of  the  top  will  pull  out  with 

1.227  X  |  X  200  X  200  =  6135  times  the  weight  of  the  material. 

132.  5.453  times  its  weight  when  on  a  level  with  the  hand ; 

4.453  times  when  highest;  6.453  times  when  lowest. 

As  this  circle  is  vertical,  the  weight  of  the  stone  acts  alternately 

with  and  against  the  centrifugal  force ;  so  that,  on  a  level  with  the 

hand,  it  pulls  (by  the  formula)  with  5.453  times  its  weight ;  but  at 

the  highest  point  with  4.453,  and  at  the  lowest  with  6.453  times. 

Page  334. 

133.  With  0.0752  of  its  weight. 

30  mi.  per  hour  is  44  ft.  per  sec.  A  circumference  of  800  ft.  radius 
measures  5026.55  ft.,  nearly.  The  force  is  therefore  1.227  X  800  x 
(5  02  e  s  s)2  =  0.0752  of  its  weight. 

134.  21.735  times  its  weight,      135.  186.116  times  its  weight. 

Page  335. 

136.  1  lb.  ;   1  lb. 

18  in.  =  I  yd.,  and  }  yd.  of  chain  =  J  lb.  weight.  Therefore,  i  lb. 
and  1  lb.  are  the  answers. 

137.  100  yds. 

The  horizontal  tension  is  25  Ibs.,  which  represents  100  yds.  of  rope. 
Hence,  radius  =  100  yds. 

138.  71f  yds. 

The  weight  of  the  rope  being  |fg  —  |  of  what  it  was,  it  takes  only 
f  of  100  yds.  =  71f  yds. 

139.  2145  Ibs. 

1980  ft.  =  660  yds.,  and  3}  x  660  =  2145  Ibs.  tension.  Ans. 

140.  !  (19.5x11.5)  -28.031  ft. 

Half-chain  =  15.5  ft.,  sag  =  4  ft. ;  sum  of  half-chain  and  sag  =  19.5, 
diff.  =  11.5.  Therefore,  by  Prop.  II.,  radius  =  1(19.5  x  11.5)  =  28.031. 


ANSWERS.  53 

141.  UL  x  28.031  —  16.27  Ibs. ;  by  III,  log  -J-  span  =  log 

19.5  +  log  11.5  +  log  (1.2900  -  1.0607)  +  colog  4  + 
0.0612  ;  whence  span  =  29.58  ;  batter  *=  1.808. 

The  chain  weighs  Jf  Ib.  to  a  ft.,  and  the  tension  is  therefore 
}f  (28.031)  =  16.27  Ibs.  By  Prop.  III.,  log  1  span  =  log  19.5  +  log  11.5 
+  log(1.2900 ~  1.0607)  +  colog 4  +  0.0612.  Whence  span  =  29.58  ft. 
By  Prop.  IV.,  batter  =  if£f!  -  1.808. 

142.  Eadius,  91.75"1;  tension,  91. 75kg;  span,  30.85m;  batter, 

5.92;  depression  at  10cm  from  ends,  1.689cm. 

Half-chain  =  15. 5m,  sag  =  1.3m;  therefore,  by  Prop.  II.,  radius  = 
16.8  X  14.2  4-  2.6  =  91.75m,  and  (by  Prop.  I.)  tension  =  91.75k«.  By 
Prop.  III.,  log  i  span  =  log  16.8  +  log  14.2  +  log  (1.2253  -  1.1523) 
+  colog  1.3 +  0.0612.  Whence  span  =  30.85m.  By  Prop.  IV.,  bat- 
ter =  9^~£  =  5.92.  10cm  now  becomes  hypotenuse  to  a  right  tri- 
angle whose  legs  are  in  the  proportion  1 :  5.92 ;  and  the  square  of 
10  =  100  is  to  be  divided  in  the  proportion  I2 :  5.922  =  1 :  35.05.  The 
smaller  of  these  parts,  2.773,  is  the  square  of  1.665cm,  the  depres- 
sion required.  The  advantage  of  logs  is  here  especially  manifest. 
Log  _L2£_  =  2  -  log  35.05  =  0.4553  ;  one-half  of  which  is  0.2277, 
which  is  log  1.689. 

143.  Suppose  the    sag   26. 5m :    it  gives,  by  III.,  half-span 

40.05 ;  suppose  the  sag  26. 6m,  it  gives  half-span 
39.95,  whence  sag  is  26.55,  as  nearly  as  four-place 
logs  can  get  it.  Batter,  0.676;  tension,  97  Ibs.  or 
44* 

Page  336. 

144.  By  position  and  Prop.  III.,  sag  =  22.55m,  and  tension 

-  111.3  Ibs. 

145.  By  position  and  Prop.  III. ,120.95  ft.;  109.96ft.;  102.6ft. 

146.  1750  gr. ;  (1728  H-  4)  x  16  -  6912,  and  sp.  gr.  =  6.912. 

147.  3.578  in.;  6.253  in. 

148.  66.45  Ibs. ;  7.673  in. 

149.  515.67  Ibs.;  15.19  in. 


54  ARITHMETIC. 

150.  7.312  in. 

2  gals,  are  462  cu.  in.  Therefore,  -f^  x  462  =  42  sq.  in.  is  the  area 
of  the  end  of  the  cylinder.  As  log  diarn.2  +  log  0.7854  =  log  42,  we 
have  2  log  diam.  =  log  42  -  log  0.7854,  or  log  diain.  -  J  (1.6232  + 
0.1049)  =  0.8640,  and  diameter  =  7.3117  inches. 

151.  8.084  in.  153.  6.2832cm.  154.  48  ft. 

152.  20.6cm.  155.  530.7  times. 

Page  337. 

156.  4.22  times  its  weight. 

The  carriage  going  at  10  mi.,  the  top  of  the  wheel  goes  at  20  mi., 
or  29  J  ft.  per  second.  The  radius  of  the  curve  is  6J  ft.,  the  total  cir- 
cumference of  which  would  be  12|  x  3.1416  =39.7936  ft.  The  force, 
therefore,  is 

1.227  X  61  x  (l^lljj)2  =  4.224  times  its  weight. 

157.  In  going  one  rnile  the  wheel  turns  530.7  times.     There- 

fore the  point  travels  3J-  X  4  X  530.7  =  6722.2  ft. 

158.  2.7761. 

A  square  shaft  to  enclose  the  neck  would  contain  6  x  6  x  7.5  = 
270ccm ;  one  to  enclose  the  body  would  contain  13  x  13  x  15.3  = 
2585. 7ccm.  A  square  frustum  would  have  its  bases  6  x  6<icm  and 
13  X  IS**6™,  and  the  square  root  of  their  product  would  be  6  x  13*icm. 
Add  the  three  and  multiply  by  i  of  7.2cm,  gives  679.2ccm.  The 
three  solids  added  make  3534. 9ccm,  which,  multiplied  by  0.7854,  to 
reduce  it  from  square  to  round  form,  gives  2776. 3ccm=  2.776  for 
the  contents. 

159.  1.251. 

Proceed  as  in  158.  The  cylinder  holds  1.62  X  8  x  0.7854ccm.  The 
frustum  Y(17.52  +  1.62  +  17.5  x  1.6)  X  0.7854ccm ;  and  the  sum  of  the 
two  is  1.251. 

160.  2.48451.  161.  33,072.6qcm;  25.7967kg. 
162.  Cap.  7.6071;  weight,  68.71kg. 

The  cavity  is  32  -  2  x  3.8  =  24.4cm  in  diameter;  and  3  times 
log  24.3  +  log  0.5236  gives  log  of  contents  in  cubic  centimeters,  that  is, 
7.6071.  The  exterior  size  is  323  x  0.5236ccm;  subtracting  cavity,  and 
multiplying  by  7.2.  gives  68.71ks  as  the  weight. 


163.  673.6qcm. 


ANSWERS.  55 

Page  338. 


On  every  side  imagine  a  multitude  of  straight  lines  going  straight 
up  the  shade.  The  space  between  any  two  would  be  measured  by 
the  product  of  its  length,  13.4cm,  and  its  average  breadth,  or  breadth 
in  the  middle.  But  these  middle  breadths  constitute  a  circumference 
round  the  shade,  with  a  diameter  J(25  +  7).  Therefore  the  curved 
surface  is  13.4  X  16  x  3.1416  -  673.6<icm. 

164.  368.611;  2.26195<r 

The  volume  of  the  half-cylinder  -  J  (0.82  X  0.7854  X  1.2).  That  of 
the  half  dome  is  J  (0.83  x  0.5236),  and  the  sum  of  the  two  -  368. 611. 
The  area  of  the  floor  is  J  (0.82  X  0.7854);  of  the  wall,  J  X  0.8  x  3.1416  x 
1.2 ;  and  of  the  roof,  }  X  4  x  0.82  x  0.7854 ;  the  sum  being  2.26195im. 

165.  9.8855". 

The  cylinder  is  3.4m  x  0.82  X  0.7854.  The  two  caps  would  make  a 
sphere,  O.S3  x  0.5236.  Half  the  sum  is  9.8855hl. 

166.  21.04  mi.  167.  23. 6G  mi. 

168.  67.8  mi. 

The  sailors'  offing  is  V52.5  miles  toward  the  coast,  and  V40,250 
miles  from  Aconcagua  ;  therefore,  200.6  -  140  =  60.6  from  the  coast, 
sind  the  ship  is  60.6  -f  7.25  =  67.85  miles  from  land. 

169.  28.5  mi. 

Page  339. 

170.  21,110  A.  (ly  logs).  174.  12.85km. 

171.  229  mi. ;  93.5  mi. ;  41.8  mi.  175.  1950m. 

172.  1429  ft. ;  5714  ft. ;  12,860  ft.  176.  8475  ft. 

173.  122.5km;  173.2km.  177.  53.88  mi. 

Page  340. 

178.  2.5946km ;  87.1667km.  181.  2.79  mi. 

179.  16  h.  3.2  min.  182.  14.16  sec. 

180.  30.63km.  183.  0.67  sec. ;  7.07  sec. 


56  ARITHMETIC. 

184.  6.93  ;  7.13  sec.  sound  ;  8.02;  9.G8  sec.,  balls;  (by  logs). 
The  wind  at  li  mi.  an  hour  goes  1G.1  ft.  a  second,  which  must  be 
added  to  the  velocity  of  the  sound  for  one  gunner,  and  subtracted  for 
the  other. 

185.  7.18  sec. 

Page  341. 
186.  $34.125.  187.  22Y2¥  min. 

188.  126,233.8  gals. 

As  the  canal  slopes  only  on  its  sides,  not  at  its  ends,  the  capacity 
is  the  same  as  if  its  top  and  bottom  were  each  7J  yds. 
50  x  7.5  x  f  -  50  x  12.5  =  625  cu.  yds. 

189.  A,  70.5;  B,  45.5  Ibs. 

190.  51f  min. 

The  man  rows  4  mi.  an  hour  for  1.2  hours ;  that  is,  rows  4.8  mi., 
but  only  makes  4  mi.  Therefore,  the  current  bears  him  down  0.8  mi. 
in  1.2  hours,  or  flows  at  f  mi.  per  hour.  When  he  rows  with  it  he 
will  therefore  go  4|  mi.  per  hour,  and  row  4  mi.  in  f  hour  =  51f  min. 

191.  40.8  ft.  193.  852.G4  sq.  in. 

192.  12T9Q-  carats;  15  carats.  194.  8.12  in. 

Page  342. 

195.  203,996  shot, 

The  cylinder  would  hold  785.398  cu.  in.  Reduce  0.3927  cu.  ft.  to 
inches  by  multiplying  by  1728,  and  subtract  from  785.398.  The 
remainder  is  what  is  lacking  ;  and  this  divided  by  O.I3  X  0.5236,  that 
is,  by  0.0005236,  will  give  the  number  of  shot. 

196.  2.353  in. 

-fa  of  231  is  3.85  cu.  in.,  the  capacity  of  a  glass.  2.5  x  2.5  x  0.785  \ 
will  be  the  area  of  the  top.  Divide  the  capacity  by  the  top  area, 
and  the  quotient  is  J  the  depth. 

197.  1  min.  9.58  sec. 

The  train  is  72  sec.  in  passing  from  one  signal  to  the  other. 
When  it  reaches  the  second  signal,  the  sound  of  the  first  signal  is 
therefore  72  X  1090.2  —  2640  ahead  of  it ;  and  this  distance,  divided 
by  1090.2,  is  72  sec.  -  2.422=  69.578  sec.,  the  required  interval. 


ANSWERS.  57 

198.  20.71 ;  29.29  yds. 

The  square  of  one  distance  is  twice  the  square  of  the  second;  the 
distances  must  therefore  be  in  the  proportion  1  :  V2,  or  1 :  1.4142  and 
2.4142 :  50  =  1 :  smaller  distance. 

199.5.366ft.;  Ifff;  (by  logs). 

The  cubical  cistern  holds  04  cu.  ft.,  and  requires  5  x  16  =  80  sq.  ft. 
of  lead  to  line  it. 

The  round  cistern  will  require  16  x  0.7854  sq.  ft.  on  the  bottom. 
Subtract  this  from  80  sq.  ft.,  and  divide  by  4  X  3.1416,  and  you  have 
the  permitted  depth.  Multiply  this  by  the  area  of  the  bottom  for 
the  capacity. 

200.  $12.60.  202.  96f  nights. 

201.  192.2  mi.  203.  22.015  in. 

Page  343. 

204.  1  long  ton  ;   2400  Ibs.  205.  9  ft. ;   7  ft.          206.  8  oz. 

207.  6  Ibs. 

The  substance  being  in  the  left  pan,  requires  9  Ibs.  in  the  right  to 
balance  it.  But  4  Ibs.  in  the  left  pan  required  the  substance  in  the 
right.  That  is,  4  Ibs.  is  to  the  substance  as  the  substance  was  to 
9  Ibs. ;  and,  by  the  rule  of  three,  4x9  =  true  weight  squared.  Hence 
the  substance  weighs  6  Ibs. 

208.  181.82  Ibs.  209.  17.68k^. 

Page  344. 

210.  Less  than  144  Ibs.  212.  88f  %  0;  11.1%  H. 

211.  Less  than  0.754  in.  213.  28f  %. 

214.  24.32%. 
Page  345. 

215.  48%.  219.  23.46  oz.  223.  831  grs. 

216.  18|f  %.  220.  52^%  ;   12%.         224.  960m*. 

217.  4T2¥%  % .  221.  40% .  225.  40K 

218.  187.6  oz.  222.  7.83  Ibs.  226.  ll,052.6g. 
227.  6530.6*.  228.  18.37%  water;  81.63%  sulphuric  acid. 
229.  2722|mg.                230.  Fe208.  231.  S02. 


58  ARITHMETIC, 

Page  ;*.  lii. 

233.  C5H8;    ll|f%. 

234.  00. 

The  numbers  actually  formed  are  those  from  10  to  99 ;  90  in  all. 
To  show  how  many  can  be  formed,  consider  that  each  digit  may  be 
followed  by  itself  or  by  either  of  the  other  9,  giving  100  sequences 
of  2  figures  ;  but  10  of  these  begin  with  naught,  and  are  to  be  reject- 
ed, leaving  90. 

235.  45. 

As  10  is  even  and  99  odd,  one-half  the  90,  —  viz.,  45,  —  is  odd. 

236.  648. 

The  digit  in  the  thousands'  place  must  be  either  1,  2,  or  3.  Either 
of  these  may  be  followed  in  the  hundreds'  place  by  either  of  the  6 
given  digits,  making  18  different  hundreds.  Each  of  these  may  be 
followed  in  the  tens'  place  by  either  of  the  6,  giving  108  different 
tens ;  each  of  which  may  have  G  digits,  giving  G48  numbers  if  you 
include  the  1000. 

237.  55. 

By  a  dominoe  is  meant  two  numbers,  side  by  side.  Double-blank 
is  00.  The  next  pieces  introducing  1  are  01,  11  ;  those  introduc- 
ing 2  are  02,  12,  22.  Every  number  introduced  requires  new 
pieces  exceeding  by  one  the  number  introduced.  Thus,  as  we  have 
seen  that  to  go  to  double-2  requires  6;  to  go  to  double-3  will  re- 
quire 6  +  4  =  10  pieces  ;  double-4,  10  +  5  =  15  pieces.  The  ordinary 
set  is  15  +  6  +  7  =  28  pieces ;  and  for  double-9's  we  should  require 
28  +  8  +  9  +  10  =  55  pieces. 

238.  31. 

With  a  single  piece,  5  amounts ;  with  2  pieces,  4  +  3  +  2  +  1  =  10 
amounts  ;  with  3  pieces,  10  amounts  ;  with  4  pieces,  5  amounts ;  with 
all  5  at  once,  1  amount ;  with  the  5  in  their  various  combinations, 
therefore,  5  + 10 +  10  + 5 +  1=31  amounts. 


MATHEMATICS. 


WENTWORTH'S    SERIES. 

HHHE  United  States  Bureau  of  Education,  in  Circular  of  Infer- 

"  mation,  No.  3,  1890,  says,  on  the  subject  of  mathematical 
text-books,  "If  we  were  called  upon  to  name  the  writer  whose 
books  have  met  with  more  wide-spread  circulation  during  the  past 
decennium  that  those  of  any  other  author,  we  should  answer, 
\Ventworth.  ...  In  point  of  scientific  rigor,  Wentworth's  books 
are  superior  to  the  popular  works  of  preceding  decades." 

These  two  points  indicate  the  two  leading  characteristics  of 
these  remarkable  books.  They  combine  mathematica.  scholarship 
with  all  the  elements  of  school-room  popularity.  The  author's 
aim  was  to  be  helpful.  He  has  made  a  study  of  his  subjects  with 
the  psychology  and  probable  capacity  of  the  students  constantly  in 
mind.  His  books  enable  the  average  student  not  merely  to  learn 
something,  but  to  master  the  study,  and  at  the  same  time  they 
give  the  brighter  ones  a  plenty  to  exercise  their  faculties  upon. 

There  is  no  attempt  to  make  a  parade  of  learning.  On  the  other 
hand,  there  is  no  absolution  from  solid  work.  Everything  is  made 
simple,  practical,  direct,  and  thorough.  Mental  energy  is  econo- 
mized. The  teacher  has  to  use  his  strength  only  in  the  necessary 
work  of  teaching,  and  the  pupil  his  only  in  the  necessary  work  of 
acquiring. 

To  learn  by  doing,  and  to  learn  one  step  thoroughly  before  the 
next  is  attempted,  are  the  chief  elements  of  the  method,  and  yet 
no  books  give  pupil  or  teacher  less  of  the  tread-mill  feeling.  The 
consciousness  of  mastery  constantly  cheers  and  invigorates  the 
student,  while  the  teacher  has  the  satisfaction  of  wielding  an  in- 
strument fitted  to  the  hand. 

All  will  recognize  in  these  characteristics  the  marks  of  ideal 
text-books.  No  one  will  claim  that  any  series  could  be  suited  to 
every  particular  case.  The  merit  of  Wentworth's  is  that  it  suits 
in  all  but  now  and  then  a  peculiar  one.  The  books  are  found 
everywhere  in  the  United  States,  and  here  and  there  all  around 
the  world.  The  testimony  of  use  may  be  summed  up  in  one  word, 
Satisfaction.  What  more  can  one  desire  than  to  be  satisfied? 

08 


70 


MATHEMATICS. 


Wentworth's  School  Algebra. 

By  G.  A.  WENTWORTH,  Professor  of  Mathematics  in  Phillips  Exeter 
Academy.  Half  morocco,  v -»- 362  pages.  Mailing  price,  31.25;  for 
introduction,  $1.12.  Answers  in  pamphlet  form,  free,  on  teachers' 
orders. 

TN"  this  book  the  author  has  availed  himself  of  his  own  expe- 
rience in  writing  and  teaching  the  elements  of  Algebra,  and  of 
the  experience  of  hundreds  of  others.  Where  improvement  was 
possible,  it  has  been  made. 

The  School  Algebra  is  offered  as  exactly  right  for  the  usual  high 
school  and  academic  courses.  It  gives  a  thorough  and  practical 
treatment  of  the  principles  of  Algebra  up  to  and  including  the 
binomial  theorem,  and  is  strictly  in  line  throughout  with  the 
author's  College  Algebra.  For  college  preparation  it  is  particu- 
larly well  suited. 

The  problems  in  this  book  are  nearly  all  new,  either  original  or 
selected  from  recent  examination  papers,  and  are  graded  with  the 
utmost  care.  They  are  sufficient  in  number  to  illustrate  and  fix 
all  the  principles,  and  interesting  and  varied  enough  to  hold  the 
student's  attention  through  the  book.  The  passage  from  Arith- 
metic to  Algebra  is  made  easy,  and  the  advantages  of  using  letters 
clearly  pointed  out.  The  treatment  of  fractions  has  been  further 
simplified.  Radicals  precede  quadratics.  There  is  at  the  end  a 
carefully  made  collection  of  miscellaneous  examples,  covering 
nearly  every  principle  of  Algebra.  This,  with  the  author's  College 
Algebra,  makes  a  complete  and  consistent  course. 

OPINIONS   OP   TEACHERS   WHO   ARE   USING   IT. 


I.  H.  Mauser,  Prin.  3IcEwensville 
Academy,  McEwensville,  Pa. :  After 
a  thorough  test  in  the  class-room  1 
can  only  say  that  I  know  of  nothing 
better.  It  is  just  the  work  to  arouse 
the  enthusiasm  and  to  bring  out  the 
thought  power  of  the  student.  It  is 
admirably  arranged  and  carefully 
graded,  and  imparts  such  a  knowl- 
edge of  elementary  algebra,  in  so 
attractive  a  way,  as  no  other  work 
does.  Too  much  cannot  be  claimed 
for  it. 

Florence  A.  Stowell  and  Mary  S. 


Cohoon,  Teachers  in  High  School, 
Binghamton,  N.  Y. :  We  are  using 
it  in  the  first  year's  work  in  our 
High  School.  We  consider  it  ex- 
cellent in  scope  and  arrangement  of 
topics,  and  better  adapted  to  our 
requirements  than  any  other  algebra 
we  have  used  or  inspected. 

A.  J.  Volland,  Principal  of  High 
School,  Racine,  Wis. :  My  opinion  of 
Wentworth's  School  Algebra  may  be 
drawn  from  the  fact  that  the  book 
is  now  in  use  in  this  school,  and  is 
uivinp;  satisfaction. 


8Q  MATHEMATICS. 

Wentworth  &  Hill's  Exercises  in  Algebra. 

I.  Exercise  Manual.  12mo.  Boards.  232  pages.  Mailing  Price,  40 
cents;  Introduction  Price,  35  cents.  II.  Examination  Manual.  12mo. 
Boards.  159  pages.  Mailing  Price,  40  cents;  Introduction  Price,  33 
cents.  Both  in  one  volume,  70  cents.  Answers  to  both  parts  together, 
25  cents. 

HpHE  first  part  (Exercise  Manual)  contains  about  4500  problems 
"*•  classified  and  arranged  according  to  the  usual  order  of  texk 
books  in  Algebra;  and  the  second  part  (Examination  Manual) 
contains  nearly  300  examination-papers,  progressive  in  charac- 
ter, and  well  adapted  to  cultivate  skill  and  rapidity  in  solving 
problems. 


British  Mail:  All  engaged  in  the 
practical  woik  of  education  will 
appreciate  these  Manuals,  as  they 
are  calculated  to  save  the  master 


much  precious  time  and  labor,  and 
to  give  his  students  the  benefit  of 
progressive  and  carefully  thought* 

out  exercises. 


Wentworth  &  Hill's  Exercises  in  Geometry. 

12mo.    Cloth.    255  pages.    Mailing  Price,  80  cents ;  Introduction  Price 
70  cents. 

rpHE  exercises  consist  of  a  great  number  of  easy  problems  foi 
beginners,  and  enough  harder  ones  for  more  advanced  pupils. 
The  problems  of  each  section  are  carefully  graded,  and  some  of  the 
more  difficult  sections  can  be  omitted  without  destroying  the  unity 
of  the  work.  The  book  can  be  used  in  connection  with  any  text- 
book on  Geometry  as  soon  as  the  geometrical  processes  of  reason- 
ing are  well  understood. 


select  propositions  from  it  to  supple« 
ment  every  stage  of  our  work. 


Amelia  W.  Platter,  High  School, 
Indianapolis,  Ind. :  I  find  the  sub- 
ject so  carefully  graded,  that  I  can 

Analytic  Geometry. 

By  G.  A.  WENTWORTH.    fievised  edition.    12mo.    Half  morocco,    xii  + 
301  pages.    Mailing  Price,  $1.35;  for  introduction,  $1.25. 

rpHE  aim  of  this  work  is  to  present  the  elementary  parts  of  the 

subject  in  the  best  form  for  class-room  use. 

The  connection  between  a  locus  and  its  equation  is  made  per- 
fectly clear  in  the  opening  chapter. 


MATHEMATICAL  TEXT-BOOKS. 

Baker  :  Elements  of  Solid  Geometry  .................................... 

Baldwin  :         Industrial  Primary  Arithmetic  ...... 

Byerly:  Differential  Calculus,  $2.00  ;  Integral  Calculus 

Fourier's  Series  ............... 

Carhart:          Field-Book,  $0.00;  Plane  Survey  in- 
Comstock  :       Method  of  Least  Squares  .................... 

Faunce  :  Descriptive  Geometry  ................ 

Gay:  Business  Book-keeping:  Single  and  Double  Entry 

Single  Entry,  .<;<J;  Double  Entry  .......................  " 

Hall:  Mensuration  ........................................................... 

Halsted  :          Metrical  Geometry  ...................................................... 

Harms  :  Determinants  .......................................................... 

Hardy:  Quaternions,  82.00;  Analytic  Geometry  ...... 

Differential  and  Integral  Calculus  .......  "  ...... 

Hill:  Geometry  for  Beginners,  81-00;  Lessons  in  Geometry 

Hyde  :  Directional  Calculus  ................................................ 

Macfarlane  :  Elementary  Mathematical  Tables  ............. 

Osborne  :          Differential  Equations  .......................................... 

Page  :  Fractions,  .30;  Teacher's  Edition  ..................................... 

Peirce  (B.  0.)  :  Newtonian  Potential  Function  .......................................... 

Peirce  (J.  M.)  :  Elements  of  Logarithms,  .50;  Mathematical  Table*. 
Prince  :  Arithmetic  by  Grades  : 

Book  I  .............................................................................. 

Teacher's  Manual  ........................................................ 

Plane  Analytic  Geometry  ...... 

Coordinate  Geometry  ............................................................ 

Elements  of  the  Calculus 


Runkle  : 

Smith  : 

Taylor  : 

Tibbets  :  College  Requirements  in  Algebra 

Wentworth  :  Primary  Arithmetic  ...............  . 

Elementary  Arithmetic  .......................................................... 

Grammar  School  Arithmetic  ......................................... 

School  Algebra.  81.12;  Higher  Algebra  ............................ 

College  Algebra  .................................................................. 

Elements  of  Algebra,  81.12;  Complete  Algebra  ........... 

New  Plane  Geometry  ............................................................ 

New  Plane  and  Solid  Geometry  ............................... 

Analytic  Geometry  .................................................................. 

Plane  Trigonometry  and  Tables  ......................................... 

Plane  and  Spherical  Trigonometry  ........................ 

Trigonometry,  Surveying,  and  Tables  ..................... 

Trigonometry,  Surveying,  and  Navigation  ..................... 

Wentworth  &  Hill:  High  School  Arithmetic  ................................. 

Exercises"in  Arithmetic,  .(SO;  Answers  ........................ 

Exercises  in  Algebra,  .70;  Answers  ............................. 

Exercises  in  Geometry  ........................................................... 

Five-place  Log.  and  Trig.  Tables  (7  Tables)  ................... 

Five-place  Log.  and  Trig.  Tables  (Complete  Edition). 
Wentworth,  McLellan  &  Glashan:  Algebraic  Analysis  ....................... 

Wentworth  &  Reed:  First  Steps  in  Number 

Teacher's  Ed.,  Complete,  .90  ;  Parts  I.,  II.,  and  III.,  eac 
Wheeler  :         Plane  and  Spherical  Trigonometry  and  Tables 


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